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Series Hilbert -curves for Dual-band and Circular Polarization Applications

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Fractal Antenna with Series Hilbert-curves for 2.45/5.35 GHz Dual-band and Circular Polarization ApplicationsSheau-Shong Bor a, Tsung-Che Lu*a, Ji-Chyun Liu b, Bing-Hao Zeng ca Dept. of Electrical Engineering, Feng Chia Universityb Dept. of Electronics Engineering, Ching Yun Universityc Dept. of Communication Engineering, Yuan Ze University229, Chien-Hsin Rd.,Jung-Li,Taiwan,R.O.Cjichyun@.twAbstract —A novel design of fractal antenna with series Hilbert-curve configuration for 2.45/5.35 GHz dual-band and circular polarization applications is presented in this paper. The compact fractal antenna consists of five series Hilbert-curve and the monopole couplings, and exhibits the desired bands 2.45 GHz (BW=85 MHz, 3.45%) and 5.35 GHz (BW=240 MHz, 4.46%) respectively. It is a compact and available monopole antenna for IEEE 802.11a/b WLAN applications. The circular polarizations for dual-band are demonstrated with AR spectrum and electric field intensities. Results included with frequency responses, radiation patterns and electric field intensities are presented and discussed.1I.I NTRODUCTIONDual-band operations in the 2.4 GHz (2.4-2.484 GHz) and 5 GHz (5.15-5.95 GHz) bands are applied to rapid developments in wireless communications. In practice, IEEE802.11b is one of WLAN with frequency band from 2.4 to 2.484 GHz for the ISM band. Hiper-LAN2 is developed with frequency bands in 5.15-5.35 GHz, 5.47-5.725 GHz and 5.725-5.925 GHz. Bands of 5.15-5.35 GHz, 5.725-5.825 GHz are applied to IEEE802.11a. The U-NII band covers the frequency band of 5.725-5.825 GHz. Besides the individual approaches among 2.4 GHz and 5.0 GHz, the requirements of 2.4/5.0 GHz dual-band antenna are necessary for applications [1]-[14], [17]-[22].For implementations, configurations such as printed dipole [1], F-shaped monopole [3], stack inverted-F monopole [2], [4], [17], double-T monopole [5], [6], rectangular slot [7], reconfigurable geometry [8], double S-shaped monopole [9], triangular slot [10], G-shaped monopole [11], C-shaped monopole [12], double ring slot [13], hock-shaped monopole [14], rectangular dielectric resonator [15], shorted parasitic patches [16], double slot-ring [18], loop monopole [19], slotted-patch monopole [20], ring monopole [21] and circular monopole [22] etc. have been developed for WLAN dual-band applications. In which, the stack inverted-F antenna usually be applied for the PCMCIA network card due to the advantage of low profile, low cost, good 50Ω matching, capable integration with circuits and easy mounted [2]. And, the modified stack inverted-F antenna was proposed to deliver the properties of diversity and improvements of frequency responses, isolation and radiation gain [4], [17]. Both the characteristics of dual-band dependent on the longer and short F-shape arms related to the 2.4 GHz lower band and 5.0 GHz higher band respectively. The compact planar loop monopole antenna was proposed for WLAN applications [19]. Recently, the dual-polarization was introduced for 5.3/5.8 GHz dual-band application [20]. However, the circular polarization of the monopole antenna has not been studied for 2.4/5.0 GHz dual-band applications.1This work was supported in part by the National Science Council in Taiwan for financially supporting this research under the Contract No. NSC 96-2623-7- 231-005-D.An alternative design of fractal antenna with Hilbert-curve configuration for 2.45/5.35 GHz dual-band and circular polarization applications is presented in this paper. Based on the iterative configuration, a novel compact monopole antenna is proposed by using the Hilbert-curve and the series configurations. The compact fractal antenna consists of five series Hilbert-curve and the monopole couplings, and exhibits the desired bands 2.45 GHz and 5.35 GHz with wider bandwidth respectively. The AR spectrum and electric field intensities are applied for demonstrating the circular polarizations for 2.45/5.35 GHz dual-bands.It is a compact and available microstrip antenna for IEEE 802.11a/b WLAN applications.II.A NTENNA C ONFIGURATION AND A NALYSISA. Fractal antenna configurationIn Fig. 1(a) and (b), the fractal antenna with series Hilbert-curve configuration and detailed Hilbert-curve dimensions are proposed respectively. The test coordinate is with the configuration in Fig. 1(c). The 50Ω microstrip feed-line is excited with a probe feed. The FR4 substrate with thickness 1.6mm and relative permittivity 4.4 is used.B. Circular polarization and electric field intensitiesFor circular polarizations, the AR spectrums are presented in Fig. 2(a) and (b). The minimum AR with 1.12 dB at θ = 100°, φ = 0° and the circular polarizations (–3dB BW = 50 MHz) are observed with a symmetrical curve for 2.45 GHz(a)(b) (c)Fig. 1 (a) Configuration of series Hilbert-curve fractal antenna.(b) Detailed dimensions of Hilbert-curve. (c) Coordinate.(a)(b)Fig. 3 Electric field intensities.band. Meantime, the minimum AR with 1.85 dB at θ = 0°, φ = 0° and the circular polarizations (–3dB BW = 75 MHz) are observed for 5.35 GHz. Thus the proposed antenna can be applied to circular polarization applications which represents one of the availabilty and usefulness in contrast to the conventional monopole antennas for 2.45/5.35 GHz dual-bands.(a)Fig. 3 illustrates the simulated electric field intensities among the planar structures, which provide a clearly physical insight on understanding the circular polarization of the proposed antenna. A typical circular polarization patch antennas usually consist of two individuals with horizontal and vertical locations, and a two-phase signal with 90° difference. Due to five Hilbert-curves are connected in vertex with orthogonal location, and the signals flow the curves with zig-zag path, therefore the circular polarization can be achieved.Fig. 3(a) shows that the series Hilbert-curve are excited at the lower -3dB resonance f=2.425 GHz and the higher -3dB resonance f=2.475GHz respectively. Fig. 3(b) shows that the series Hilbert-curve are excited at the lower -3dB(b)Fig. 2 AR spectrums. (a) 2.45 GHz band, (b) 5.35 GHz band(a)Fig. 5 Radiation patterns for 2.45 GHz.(b)Fig. 4 Simulated and measured results of S 11 spectrum(a) at 2.45 GHz band (b) at 5.35 GHz band.resonance f=5.290 GHz and the higher -3dB resonance f=5.365 GHz respectively. The currents flow with zig-zag way along the Hilbert-curves, therefore the circular polarization can be observed.III. S IMULATION & RESULTSA. S-parameters frequency responsesTo analyze the resonant frequencies, the S 11 return loss spectrums are simulated and measured in Fig. 4 (a) and (b) for 2.45/5.35 GHz dual-band respectively. By using the commercial software of HFSS tool, the simulation results are also presented and analyzed. It is evident that the simulated and measured results of frequency responses are in agreement. In measurement, while the return loss is smaller than -10dB, the frequency responses cover two bands, from 2.425 to 2.51 GHz (bandwidth = 85 MHz, 3.45%), and from 5.26 to 5.50 GHz (bandwidth = 240 MHz, 4.46%). For applications, the frequency responses are covered in the operation bands of the IEEE802.11a/b and the U-NII band.Fig. 6 Radiation patterns for 5.35 GHz.B. Abbreviations and AcronymsIn field analyses, the radiation patterns are obtained by an automatic measurement system in an anechoic chamber. For the field coordinates shown in Fig. 1(c), the under-tested antenna is located on the X-Y plane, and the feeding line is located along the Y-axis. Thus, radiation patterns with X-Y cut, X-Z cut and Y-Z cut are obtained.Fig. 7 Radiation power gains.The three cut patterns with resonant 2.45 GHz and 5.35 GHz are represented in Fig. 5 as well as in Fig. 6 respectively. In Fig. 5, broadside patterns are observed in the X-Y cut and X-Z cut (solid line φ = 0°, θ = varied), and omnidirectional patterns are obtained in the Y-Z cut (solid line φ = 0°, θ = varied) for 2.45 GHz band. Related smaller directive radiation patterns are shown in X-Y cut, X-Z cut and Y-Z cut (dash lineθ = 0°, φ = varied). It can be applied for the monopole applications. The peak radiation power gains are presented in Fig. 7 with 2.0-3.4 dBi.In Fig. 6, slightly broadside patterns are observed in the X-Y cut and X-Z cut (φ = 0°, θ = varied), and omnidirectional patterns are obtained in the Y-Z cut (φ = 0°, θ = varied) for 5.35 GHz band. Related larger directive radiation patterns are shown in X-Y cut, X-Z cut and Y-Z cut (θ = 0°, φ = varied). It can be applied for the quasi-monopole applications. The peak radiation power gains are presented in Fig. 7 with 0.6-1.1 dBi.IV.C ONCLUSIONThe fractal antenna with series Hilbert-curve configuration for 2.45/5.35GHz dual-band applications is presented in this paper. The structure is smaller in size and easy to fabricate in PCMCIA circuits. The configuration of the five series Hilbert-curve configuration determines the lower band of 2.45 GHz and the higher band of 5.35 GHz simultaneously. Its operations simultaneously cover two bands of 2.45 GHz (85 MHz, 3.45%), and 5.35 GHz (240 MHz, 4.46%) for return loss ＜-10dB. Both simulation and measurement results agreed with the verified frequency responses. The AR spectrum and electric field intensities are applied for demonstrating the circular polarizations for 2.45/5.35 GHz dual-bands.It is a compact and available microstrip antenna for IEEE 802.11a/b WLAN applications. The broadside patterns presented in the X-Y cut and X-Z cut planes, and omnidirectional pattern is obtained in the Y-Z cut plane for 2.45 GHz band can be applied for the monopole applications. The peak radiation power gains are with 2.0-3.4 dBi. Slightly broadside patterns observed in the X-Y cut and X-Z cut planes, and omnidirectional patterns obtained in the Y-Z cut plane for 5.35 GHz band can be applied for the quasi-monopole applications. The peak radiation power gains are with 0.6-1.1 dBi.R EFERENCES[1]Y. H. Suh and K. Chang, “Low cost microstrip-fed dual frequencyprinted dipole antenna for wireless communications,” Electron Lett,36, 2000, pp.1177- 1179.[2]Y. L. Kuo, T. W. Chiou, and K. L. Wong, “A novel dual-band printedI nverted-F antenna,” Microwave Opt Technol Lett., 31, 2001, pp.353-355.[3]S. H. Yeh and and K. L. Wong, “Integrated F-shaped monopoleantenna for 2.4/5.2 GHz dual-band operation,” Microwave Opt Technol Lett, 34, 2002, pp.24-26.[4]K. L. Wong, Y. Y. Chen, S. W. Su, and Y. L. Kuo, “Diversity dual-band planar inverted-F antenna for WLAN operation,” MicrowaveOpt Technol Lett , 38, 2003, pp.223-225. [5]Y. L. Kuo and K. L. Wong, “Printed double-T monopole antenna for2.4/5.2 GHz dual-band WLAN operations,” IEEE Trans AntennasPropagat., 51, 2003, pp.2187-2192.[6]T. Y. Wu, S. T. Fang, and K. L. Wong, “A printed diversity dual-bandmonopole antenna for WLAN operation in the 2.4- and 5.2-GHz bands,” Microwave Opt Technol Lett., 36, 2003, pp.436-439.[7]J. W. Wu, H. M. Hsiao, J. H. Lu, and S. H. Chang, “Dual broadbanddesign of rectangular slot antenna for 2.4 and 5GHz wireless communication,” Electron Lett., 40, 2004, pp.1463-1464.[8]W. H. Chen, Z. H. Feng, M. Y. Fan and Y. Furuya, “Dual-bandreconfigurable antenna for wireless communications,” Microwave Opt Technol Lett., 40, 2004, pp.503-505.[9]W. C. Liu, W. R. Chen, and C. M. Wu, “Printed double S-shapedmonopole antenna for wideband and multiband operation of wireless communications,” IEE Proc-Microw Antennas Propag., 151, 2004, pp.473-476.[10]J. S. Wu, “2.4/5 GHz dual-band triangular slot antenna with compactoperation,” Microwave Opt Technol Lett., 45, 2005, pp.81-84.[11] C. Y. Pan, C. H. Huang, and T. S. Hormg, “A new printed G-shapedmonopole antenna for dual-band WLAN applications,” Microwave Opt Technol Lett., 45, 2005, pp.295-297.[12]G. Chi, B. Li, and D. Qi, “Dual-band printed diversity antenna for2.4/5.2-GHz WLAN application,” Microwave Opt Technol Lett., 45,2005, pp.561-563.[13]J. C. Liu, B. H. Zeng, C. Y. Wu and D. C. Chang, “Double-ring slotantenna with tree-shaped coupling strip for WLAN 2.4/5 GHz dual-band applications,” Microwave Opt Technol Lett., 47, 2005, pp.374-379.[14] C. H. Lee and S. O. Park, “A compact printed hock-shaped monopoleantenna for 2.4/5-GHz WLAN applications,” Microwave Opt Technol Lett., 48, 2006, pp.327-329.[15] E. H. Lim and K. W. Leung, “Dual-wideband rectangular dielectricresonator antenna for WLAN communications,” Microwave Opt Technol Lett., 48, 2006, pp.378-380.[16]M. Multari and R. Staraj, “Wideband miniature antenna for IEEE802.11 a and 11b WLAN standards,” Microwave Opt Technol Lett., 48, 2006, pp.590-593.[17] C. P. Liu, J. C. Wu and J. C. Liu, “Modified stack inverted-F antennawith corner-truncated techniques for WLAN 2.4/5 GHz band applications,” Microwave Opt. Technol Lett., 48, 2006, pp.378-2381. [18]J. C. Liu, B. H. Zeng, C. Y. Wu and D. C. Chang, “A synthesistechnique of double-ring slot antenna with tree-shaped coupling strip for dual broad-band applications,” IEE Proc-Microw Antennas Propag., 154, 2006, pp.510-515.[19]M. Bledowski and M. Kitlinski, “Compact planar monopole loopantennas for 802.11 b/g WLAN systems,” Microwave Opt. Technol Lett., 49, 2007, pp.2299-2303.[20]V. P. Sarin, M. S. Nishamol, G. Augustin, P. Mohanan, C. K.Aanandan, and K. Vasudevan, “An electromagnetically coupled dual-band dual-polarized microstrip antenna for WLAN applications,”Microwave and Opt. Technol. Lett., 50, 2008, pp.1867-1870.[21]L. Zhang, Y. C. Jiao, G. Zhao, Y. Song, and F. S. Zhang, “Broadbanddual-band cpw-fed closed rectangular ring monopole antenna with a vertical strip for WLAN operation,” Microwave and Opt. Technol.Lett., 50, 2008, pp.1929-1937.[22] F. S. Chang, K. C. Chao, C. H. Lu and S. W. Su, “Compact verticalpatch antenna for dual-band WLAN operation,” Electronics Letters, 44, 2008, pp.612-613.。

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线性代数_常用单词词组_中英对照

线性代数_常用单词词组_中英对照

Dual problem对偶问题442,446EEconomics 经济学435,439Eigencourse 457,458Eigenvalue 特征值283,287,374,499 Eigenvalue changes 特征值变换439284,294,300 Eigenvalues of 的特征值297Eigenvalues of 的特征值362Eigenvalues of 的特征值Eigenvector basis 基底的特征向量399Eigenvectors 特征向量283,287,374Eigshow 290,368Elimination 消元法45-66,83,86,135Ellipse 椭圆290,346,366,382Energy 能量343,409Engineering 工程409,419Error 误差211,218,219,225,481,483 Error equation 误差方程477Euler angles 欧拉角474Euler’s formula 欧拉公式311,426,430,497Even 偶数113,246,258,452 Exponential 指数的314,319,327FFactorization 因式分解95,110,235,348,370,374 False proof 假证明305,338Fast Fourier Transform 快速傅立叶变换393,493,511,565Feasible set 可行集440,441FFT(see Fast见快速傅里叶变换509-514Fourier Transform)Fibonacci 菲波那契75,266,268,301,302,306,308 Finite difference 有限差分315-317,417Finite elements 有限元412,419First-order system 一阶方程组315,326Fixed-free 固定-自由410,414,417,419Force balance 平衡力412FORTRAN 16,38Forward difference 前向差分30Four Fundamental Subspaces 四个基本子空间184-199,368,424,507 Fourier series 傅立叶序列233,448,450,452Fourier Transform 傅立叶变换393,509-514Fredholm Alternative 弗雷德霍姆择一203Free 自由133,135,137,144,146,155 Full column rank 列满秩157,170,405Full row rank 行满秩159,405Function space 函数空间121,448,449 Fundamental Theorem of Linear线性代数基本定理188,198,368Algebra(see Four Fundamental Subspaces)GGaussian elimination 高斯消元法45,49,135Gaussian probability distribution 高斯概率分布455Gauss-Jordan 高斯-约当83,84,91,469Gauss-Seidel 高斯-塞德尔481,484,485,489Gene expression data 基因表达数据457Geometric series 等比数列436Gershgorin circles 格尔什戈林圆491Gibbs phenomenon 吉布斯效应451Givens rotation 吉文斯旋转471Google 谷歌368,369,434Gram-Schmidt 格拉姆-施密特223,234,236,241,370,469 Graph 图表74,143,307,311,420,422,423 Group 群119,354HHalf-plane 半平面7Heat equation 热方程式322,323Heisenberg 海森堡305,310Hilbert space 希尔伯特空间447,449Hook e’s Law 虎克定律410,412Householder reflections 镜像变换237,469,472Hyperplane 超平面30,42IIll-conditioned matrix 病态矩阵371,473,474Imaginary 虚数289Independent 独立的26,27,134,168,200,300 Initial value 初值313Inner product 内积11,56,108,448,502,506 Input and output basis 基底输入输出399Integral 积分24,385,386Interior point method 内点法445Intersection of spaces 交空间129,183Inverse matrix 逆矩阵24,81,27082Inverse of的逆Invertible 可逆的86,173,200,248Iteration 迭代481,482,484,489,492JJacobi 雅可比481,483,485,489Jordan form 约当型356,357,358,361,482 JPEG 364,373KKalman filter 卡尔曼滤波器93,214Kernel 核377,380Kirchhoff’s Laws 基尔霍夫定律143,189,420,424-427 Krylov 克雷洛夫491,492L225,480norm 和范数Lagrange multiplier 拉格朗日乘子445Lanczos method 兰索斯方法490,492LAPACK 线性代数软件包98,237,486Leapfrog method 跳步法317,329Least squares 最小平方218,219,236,405,408,453184,186,192,425Left nullspace左零空间Left-inverse 左逆的81,86,154,405Length 长度12,232,447,448,501Line 线34,40,221,474Line of springs 线弹簧411Linear combination 线性组合1,3Linear equation 线性方程23Linear programming 线性规划440Linear transformation 线性变换44,375-398Linearity 线性关系44,245,246Linearly independent 线性独立26,134,168,169,200 LINPACK 线性系统软件包465Loop 环路307,425,426Lower triangular 下三角9598,100,474Lucas numbers 卢卡斯数306MMaple 38,100Mathematica 38,100MATLAB 17,37,237,243,290,337,513 Matrix(see full page 570) 矩阵22,384,387Matrix exponential 矩阵指数314,319,32711。

线性代数-常用单词词组-中英对照

线性代数-常用单词词组-中英对照

Dual problem对偶问题442,446EEconomics 经济学435,439Eigencourse 457,458Eigenvalue 特征值283,287,374,499 Eigenvalue changes 特征值变换439284,294,300 Eigenvalues of 的特征值297Eigenvalues of 的特征值362Eigenvalues of 的特征值Eigenvector basis 基底的特征向量399Eigenvectors 特征向量283,287,374Eigshow 290,368Elimination 消元法45-66,83,86,135Ellipse 椭圆290,346,366,382Energy 能量343,409Engineering 工程409,419Error 误差211,218,219,225,481,483 Error equation 误差方程477Euler angles 欧拉角474Euler’s formula 欧拉公式311,426,430,497Even 偶数113,246,258,452 Exponential 指数的314,319,327FFactorization 因式分解95,110,235,348,370,374 False proof 假证明305,338Fast Fourier Transform 快速傅立叶变换393,493,511,565Feasible set 可行集440,441FFT(see Fast见快速傅里叶变换509-514Fourier Transform)Fibonacci 菲波那契75,266,268,301,302,306,308 Finite difference 有限差分315-317,417Finite elements 有限元412,419First-order system 一阶方程组315,326Fixed-free 固定-自由410,414,417,419Force balance 平衡力412FORTRAN 16,38Forward difference 前向差分30Four Fundamental Subspaces 四个基本子空间184-199,368,424,507 Fourier series 傅立叶序列233,448,450,452Fourier Transform 傅立叶变换393,509-514Fredholm Alternative 弗雷德霍姆择一203Free 自由133,135,137,144,146,155 Full column rank 列满秩157,170,405Full row rank 行满秩159,405Function space 函数空间121,448,449 Fundamental Theorem of Linear线性代数基本定理188,198,368Algebra(see Four Fundamental Subspaces)GGaussian elimination 高斯消元法45,49,135Gaussian probability distribution 高斯概率分布455Gauss-Jordan 高斯-约当83,84,91,469Gauss-Seidel 高斯-塞德尔481,484,485,489Gene expression data 基因表达数据457Geometric series 等比数列436Gershgorin circles 格尔什戈林圆491Gibbs phenomenon 吉布斯效应451Givens rotation 吉文斯旋转471Google 谷歌368,369,434Gram-Schmidt 格拉姆-施密特223,234,236,241,370,469 Graph 图表74,143,307,311,420,422,423 Group 群119,354HHalf-plane 半平面7Heat equation 热方程式322,323Heisenberg 海森堡305,310Hilbert space 希尔伯特空间447,449Hook e’s Law 虎克定律410,412Householder reflections 镜像变换237,469,472Hyperplane 超平面30,42IIll-conditioned matrix 病态矩阵371,473,474Imaginary 虚数289Independent 独立的26,27,134,168,200,300 Initial value 初值313Inner product 内积11,56,108,448,502,506 Input and output basis 基底输入输出399Integral 积分24,385,386Interior point method 内点法445Intersection of spaces 交空间129,183Inverse matrix 逆矩阵24,81,27082Inverse of的逆Invertible 可逆的86,173,200,248Iteration 迭代481,482,484,489,492JJacobi 雅可比481,483,485,489Jordan form 约当型356,357,358,361,482 JPEG 364,373KKalman filter 卡尔曼滤波器93,214Kernel 核377,380Kirchhoff’s Laws 基尔霍夫定律143,189,420,424-427 Krylov 克雷洛夫491,492L225,480norm 和范数Lagrange multiplier 拉格朗日乘子445Lanczos method 兰索斯方法490,492LAPACK 线性代数软件包98,237,486Leapfrog method 跳步法317,329Least squares 最小平方218,219,236,405,408,453184,186,192,425Left nullspace左零空间Left-inverse 左逆的81,86,154,405Length 长度12,232,447,448,501Line 线34,40,221,474Line of springs 线弹簧411Linear combination 线性组合1,3Linear equation 线性方程23Linear programming 线性规划440Linear transformation 线性变换44,375-398Linearity 线性关系44,245,246Linearly independent 线性独立26,134,168,169,200 LINPACK 线性系统软件包465Loop 环路307,425,426Lower triangular 下三角9598,100,474Lucas numbers 卢卡斯数306MMaple 38,100Mathematica 38,100MATLAB 17,37,237,243,290,337,513 Matrix(see full page 570) 矩阵22,384,387Matrix exponential 矩阵指数314,319,327Matrix multiplication 矩阵乘法58,59,67,389----。

4EI

4EI

检索示例姓名：李芬芬学号： 08121499练习数据库： CompendexWeb练习题目：关于”自适应滤波器”方面的相关文献1．分析检索概念，拟定检索策略：1）分析检索概念本课题的主要概念为“适应”“滤波器”,对应的英语单词为:适应：adaptation，accommodate滤波器: filter, FLT，FILT，FLTR filter2）拟定检索策略(adaptation or accommodate) and （filter or FLT * or FLTR filter ）2．快速检索界面(Quick Search)检索选项设置取默认状态，以上策略的系统响应为：37173 records in Compendex for 1969-2010 (((adaptation or accommodate) WN KY) AND ((filter or FLT *or FLTR filter) WN KY))37173篇3. 专家检索界面（Expert Search）将上述策略中的AND用NEAR或ONEAR代替，优先符中取一个词，字段取TI或AB调整后的检索策略为：(adaptation ONEAR filter) wn TI系统响应为：176 records in Compendex for 1969-2010 (adaptation ONEAR filter) wn TI选取其中一篇切题文献的题录(篇名.著者（单位）.来源出处)信息如下Adaptation of the filter furnace atomizer for atomic absorption determination of less volatile metalsKatskov, D.A. (Technikon Pretoria, Pretoria, South Africa); Marais, P.J.J.G.; Katkovnik, V.J.; Tittarelli, P. Source: Spectrochimica acta, Part B: Atomic spectroscopy, v 52, n 9-10, p 1377-1394, Jul 30 1997从检索结果右栏的controlled vocabulary中选取合适的主题词为：information retrieval 4. 主题词表途径检索(Thesaurus)使用上步选取的叙词 information retrieval，检索Thesaurus主题词表。

量子力学索引英汉对照

量子力学索引英汉对照

21-centimeter line, 21厘米线AAbsorption, 吸收Addition of angular momenta, 角动量叠加Adiabatic approximation, 绝热近似Adiabatic process, 绝热过程Adjoint, 自伴的Agnostic position, 不可知论立场Aharonov-Bohm effect, 阿哈罗诺夫-玻姆效应Airy equation, 艾里方程；Airy function, 艾里函数Allowed energy, 允许能量Allowed transition, 允许跃迁Alpha decay, 衰变；Alpha particle, 粒子Angular equation, 角向方程Angular momentum, 角动量Anomalous magnetic moment, 反常磁矩Antibonding, 反键Anti-hermitian operator, 反厄米算符Associated Laguerre polynomial, 连带拉盖尔多项式Associated Legendre function, 连带勒让德多项式Atoms, 原子Average value, 平均值Azimuthal angle, 方位角Azimuthal quantum number, 角量子数BBalmer series, 巴尔末线系Band structure, 能带结构Baryon, 重子Berry's phase, 贝利相位Bessel functions, 贝塞尔函数Binding energy, 束缚能Binomial coefficient, 二项式系数Biot-Savart law, 毕奥-沙法尔定律Blackbody spectrum, 黑体谱Bloch's theorem, 布洛赫定理Bohr energies, 玻尔能量；Bohr magneton, 玻尔磁子；Bohr radius, 玻尔半径Boltzmann constant, 玻尔兹曼常数Bond, 化学键Born approximation, 玻恩近似Born's statistical interpretation, 玻恩统计诠释Bose condensation, 玻色凝聚Bose-Einstein distribution, 玻色-爱因斯坦分布Boson, 玻色子Bound state, 束缚态Boundary conditions, 边界条件Bra, 左矢Bulk modulus, 体积模量CCanonical commutation relations, 正则对易关系Canonical momentum, 正则动量Cauchy's integral formula, 柯西积分公式Centrifugal term, 离心项Chandrasekhar limit, 钱德拉赛卡极限Chemical potential, 化学势Classical electron radius, 经典电子半径Clebsch-Gordan coefficients, 克-高系数Coherent States, 相干态Collapse of wave function, 波函数塌缩Commutator, 对易子Compatible observables, 对易的可观测量Complete inner product space, 完备内积空间Completeness, 完备性Conductor, 导体Configuration, 位形Connection formulas, 连接公式Conservation, 守恒Conservative systems, 保守系Continuity equation, 连续性方程Continuous spectrum, 连续谱Continuous variables, 连续变量Contour integral, 围道积分Copenhagen interpretation, 哥本哈根诠释Coulomb barrier, 库仑势垒Coulomb potential, 库仑势Covalent bond, 共价键Critical temperature, 临界温度Cross-section, 截面Crystal, 晶体Cubic symmetry, 立方对称性Cyclotron motion, 螺旋运动DDarwin term, 达尔文项de Broglie formula, 德布罗意公式de Broglie wavelength, 德布罗意波长Decay mode, 衰变模式Degeneracy, 简并度Degeneracy pressure, 简并压Degenerate perturbation theory, 简并微扰论Degenerate states, 简并态Degrees of freedom, 自由度Delta-function barrier, 势垒Delta-function well, 势阱Derivative operator, 求导算符Determinant, 行列式Determinate state, 确定的态Deuterium, 氘Deuteron, 氘核Diagonal matrix, 对角矩阵Diagonalizable matrix, 对角化Differential cross-section, 微分截面Dipole moment, 偶极矩Dirac delta function, 狄拉克函数Dirac equation, 狄拉克方程Dirac notation, 狄拉克记号Dirac orthonormality, 狄拉克正交归一性Direct integral, 直接积分Discrete spectrum, 分立谱Discrete variable, 离散变量Dispersion relation, 色散关系Displacement operator, 位移算符Distinguishable particles, 可分辨粒子Distribution, 分布Doping, 掺杂Double well, 双势阱Dual space, 对偶空间Dynamic phase, 动力学相位EEffective nuclear charge, 有效核电荷Effective potential, 有效势Ehrenfest's theorem, 厄伦费斯特定理Eigenfunction, 本征函数Eigenvalue, 本征值Eigenvector, 本征矢Einstein's A and B coefficients, 爱因斯坦A,B系数；Einstein's mass-energy formula, 爱因斯坦质能公式Electric dipole, 电偶极Electric dipole moment, 电偶极矩Electric dipole radiation, 电偶极辐射Electric dipole transition, 电偶极跃迁Electric quadrupole transition, 电四极跃迁Electric field, 电场Electromagnetic wave, 电磁波Electron, 电子Emission, 发射Energy, 能量Energy-time uncertainty principle, 能量-时间不确定性关系Ensemble, 系综Equilibrium, 平衡Equipartition theorem, 配分函数Euler's formula, 欧拉公式Even function, 偶函数Exchange force, 交换力Exchange integral, 交换积分Exchange operator, 交换算符Excited state, 激发态Exclusion principle, 不相容原理Expectation value, 期待值FFermi-Dirac distribution, 费米-狄拉克分布Fermi energy, 费米能Fermi surface, 费米面Fermi temperature, 费米温度Fermi's golden rule, 费米黄金规则Fermion, 费米子Feynman diagram, 费曼图Feynman-Hellman theorem, 费曼-海尔曼定理Fine structure, 精细结构Fine structure constant, 精细结构常数Finite square well, 有限深方势阱First-order correction, 一级修正Flux quantization, 磁通量子化Forbidden transition, 禁戒跃迁Foucault pendulum, 傅科摆Fourier series, 傅里叶级数Fourier transform, 傅里叶变换Free electron, 自由电子Free electron density, 自由电子密度Free electron gas, 自由电子气Free particle, 自由粒子Function space, 函数空间Fusion, 聚变Gg-factor, g-因子Gamma function, 函数Gap, 能隙Gauge invariance, 规范不变性Gauge transformation, 规范变换Gaussian wave packet, 高斯波包Generalized function, 广义函数Generating function, 生成函数Generator, 生成元Geometric phase, 几何相位Geometric series, 几何级数Golden rule, 黄金规则"Good" quantum number, "好"量子数"Good" states, "好"的态Gradient, 梯度Gram-Schmidt orthogonalization, 格莱姆-施密特正交化法Graphical solution, 图解法Green's function, 格林函数Ground state, 基态Group theory, 群论Group velocity, 群速Gyromagnetic railo, 回转磁比值HHalf-integer angular momentum, 半整数角动量Half-life, 半衰期Hamiltonian, 哈密顿量Hankel functions, 汉克尔函数Hannay's angle, 哈内角Hard-sphere scattering, 硬球散射Harmonic oscillator, 谐振子Heisenberg picture, 海森堡绘景Heisenberg uncertainty principle, 海森堡不确定性关系Helium, 氦Helmholtz equation, 亥姆霍兹方程Hermite polynomials, 厄米多项式Hermitian conjugate, 厄米共轭Hermitian matrix, 厄米矩阵Hidden variables, 隐变量Hilbert space, 希尔伯特空间Hole, 空穴Hooke's law, 胡克定律Hund's rules, 洪特规则Hydrogen atom, 氢原子Hydrogen ion, 氢离子Hydrogen molecule, 氢分子Hydrogen molecule ion, 氢分子离子Hydrogenic atom, 类氢原子Hyperfine splitting, 超精细分裂IIdea gas, 理想气体Idempotent operaror, 幂等算符Identical particles, 全同粒子Identity operator, 恒等算符Impact parameter, 碰撞参数Impulse approximation, 脉冲近似Incident wave, 入射波Incoherent perturbation, 非相干微扰Incompatible observables, 不对易的可观测量Incompleteness, 不完备性Indeterminacy, 非确定性Indistinguishable particles, 不可分辨粒子Infinite spherical well, 无限深球势阱Infinite square well, 无限深方势阱Inner product, 内积Insulator, 绝缘体Integration by parts, 分部积分Intrinsic angular momentum, 内禀角动量Inverse beta decay, 逆衰变Inverse Fourier transform, 傅里叶逆变换KKet, 右矢Kinetic energy, 动能Kramers' relation, 克莱默斯关系Kronecker delta, 克劳尼克LLCAO technique, 原子轨道线性组合法Ladder operators, 阶梯算符Lagrange multiplier, 拉格朗日乘子Laguerre polynomial, 拉盖尔多项式Lamb shift, 兰姆移动Lande g-factor, 朗德g-因子Laplacian, 拉普拉斯的Larmor formula, 拉摩公式Larmor frequency, 拉摩频率Larmor precession, 拉摩进动Laser, 激光Legendre polynomial, 勒让德多项式Levi-Civita symbol, 列维-西维塔符号Lifetime, 寿命Linear algebra, 线性代数Linear combination, 线性组合Linear combination of atomic orbitals, 原子轨道的线性组合Linear operator, 线性算符Linear transformation, 线性变换Lorentz force law, 洛伦兹力定律Lowering operator, 下降算符Luminoscity, 照度Lyman series, 赖曼线系MMagnetic dipole, 磁偶极Magnetic dipole moment, 磁偶极矩Magnetic dipole transition, 磁偶极跃迁Magnetic field, 磁场Magnetic flux, 磁通量Magnetic quantum number, 磁量子数Magnetic resonance, 磁共振Many worlds interpretation, 多世界诠释Matrix, 矩阵；Matrix element, 矩阵元Maxwell-Boltzmann distribution, 麦克斯韦-玻尔兹曼分布Maxwell's equations, 麦克斯韦方程Mean value, 平均值Measurement, 测量Median value, 中位值Meson, 介子Metastable state, 亚稳态Minimum-uncertainty wave packet, 最小不确定度波包Molecule, 分子Momentum, 动量Momentum operator, 动量算符Momentum space wave function, 动量空间波函数Momentum transfer, 动量转移Most probable value, 最可几值Muon, 子Muon-catalysed fusion, 子催化的聚变Muonic hydrogen, 原子Muonium, 子素NNeumann function, 纽曼函数Neutrino oscillations, 中微子振荡Neutron star, 中子星Node, 节点Nomenclature, 术语Nondegenerate perturbationtheory, 非简并微扰论Non-normalizable function, 不可归一化的函数Normalization, 归一化Nuclear lifetime, 核寿命Nuclear magnetic resonance, 核磁共振Null vector, 零矢量OObservable, 可观测量Observer, 观测者Occupation number, 占有数Odd function, 奇函数Operator, 算符Optical theorem, 光学定理Orbital, 轨道的Orbital angular momentum, 轨道角动量Orthodox position, 正统立场Orthogonality, 正交性Orthogonalization, 正交化Orthohelium, 正氦Orthonormality, 正交归一性Orthorhombic symmetry, 斜方对称Overlap integral, 交叠积分PParahelium, 仲氦Partial wave amplitude, 分波幅Partial wave analysis, 分波法Paschen series, 帕邢线系Pauli exclusion principle, 泡利不相容原理Pauli spin matrices, 泡利自旋矩阵Periodic table, 周期表Perturbation theory, 微扰论Phase, 相位Phase shift, 相移Phase velocity, 相速Photon, 光子Planck's blackbody formula, 普朗克黑体辐射公式Planck's constant, 普朗克常数Polar angle, 极角Polarization, 极化Population inversion, 粒子数反转Position, 位置；Position operator, 位置算符Position-momentum uncertainty principles, 位置-动量不确定性关系Position space wave function, 坐标空间波函数Positronium, 电子偶素Potential energy, 势能Potential well, 势阱Power law potential, 幂律势Power series expansion, 幂级数展开Principal quantum number, 主量子数Probability, 几率Probability current, 几率流Probability density, 几率密度Projection operator, 投影算符Propagator, 传播子Proton, 质子QQuantum dynamics, 量子动力学Quantum electrodynamics, 量子电动力学Quantum number, 量子数Quantum statics, 量子统计Quantum statistical mechanics, 量子统计力学Quark, 夸克RRabi flopping frequency, 拉比翻转频率Radial equation, 径向方程Radial wave function, 径向波函数Radiation, 辐射Radius, 半径Raising operator, 上升算符Rayleigh's formula, 瑞利公式Realist position, 实在论立场Recursion formula, 递推公式Reduced mass, 约化质量Reflected wave, 反射波Reflection coefficient, 反射系数Relativistic correction, 相对论修正Rigid rotor, 刚性转子Rodrigues formula, 罗德里格斯公式Rotating wave approximation, 旋转波近似Rutherford scattering, 卢瑟福散射Rydberg constant, 里德堡常数Rydberg formula, 里德堡公式SScalar potential, 标势Scattering, 散射Scattering amplitude, 散射幅Scattering angle, 散射角Scattering matrix, 散射矩阵Scattering state, 散射态Schrodinger equation, 薛定谔方程Schrodinger picture, 薛定谔绘景Schwarz inequality, 施瓦兹不等式Screening, 屏蔽Second-order correction, 二级修正Selection rules, 选择定则Semiconductor, 半导体Separable solutions, 分离变量解Separation of variables, 变量分离Shell, 壳Simple harmonic oscillator, 简谐振子Simultaneous diagonalization, 同时对角化Singlet state, 单态Slater determinant, 斯拉特行列式Soft-sphere scattering, 软球散射Solenoid, 螺线管Solids, 固体Spectral decomposition, 谱分解Spectrum, 谱Spherical Bessel functions, 球贝塞尔函数Spherical coordinates, 球坐标Spherical Hankel functions, 球汉克尔函数Spherical harmonics, 球谐函数Spherical Neumann functions, 球纽曼函数Spin, 自旋Spin matrices, 自旋矩阵Spin-orbit coupling, 自旋-轨道耦合Spin-orbit interaction, 自旋-轨道相互作用Spinor, 旋量Spin-spin coupling, 自旋-自旋耦合Spontaneous emission, 自发辐射Square-integrable function, 平方可积函数Square well, 方势阱Standard deviation, 标准偏差Stark effect, 斯塔克效应Stationary state, 定态Statistical interpretation, 统计诠释Statistical mechanics, 统计力学Stefan-Boltzmann law, 斯特番-玻尔兹曼定律Step function, 阶跃函数Stem-Gerlach experiment, 斯特恩-盖拉赫实验Stimulated emission, 受激辐射Stirling's approximation, 斯特林近似Superconductor, 超导体Symmetrization, 对称化Symmetry, 对称TTaylor series, 泰勒级数Temperature, 温度Tetragonal symmetry, 正方对称Thermal equilibrium, 热平衡Thomas precession, 托马斯进动Time-dependent perturbation theory, 含时微扰论Time-dependent Schrodinger equation, 含时薛定谔方程Time-independent perturbation theory, 定态微扰论Time-independent Schrodinger equation, 定态薛定谔方程Total cross-section, 总截面Transfer matrix, 转移矩阵Transformation, 变换Transition, 跃迁；Transition probability, 跃迁几率Transition rate, 跃迁速率Translation,平移Transmission coefficient, 透射系数Transmitted wave, 透射波Trial wave function, 试探波函数Triplet state, 三重态Tunneling, 隧穿Turning points, 回转点Two-fold degeneracy , 二重简并Two-level systems, 二能级体系UUncertainty principle, 不确定性关系Unstable particles, 不稳定粒子VValence electron, 价电子Van der Waals interaction, 范德瓦尔斯相互作用Variables, 变量Variance, 方差Variational principle, 变分原理Vector, 矢量Vector potential, 矢势Velocity, 速度Vertex factor, 顶角因子Virial theorem, 维里定理WWave function, 波函数Wavelength, 波长Wave number, 波数Wave packet, 波包Wave vector, 波矢White dwarf, 白矮星Wien's displacement law, 维恩位移定律YYukawa potential, 汤川势ZZeeman effect, 塞曼效应。