By Zhuangqi Cao, Cheng Yin
Advances in One-Dimensional Wave Mechanics presents a accomplished description of the movement of microscopic debris in one-dimensional, arbitrary-shaped potentials in line with the analogy among Quantum Mechanics and Electromagnetism. using a deeper figuring out of the wave nature of subject, this booklet introduces the idea that of the scattered sub-waves and a chain of latest analytical effects utilizing the Analytical move Matrix (ATM) procedure. This paintings could be invaluable for graduate scholars majoring in physics, mostly in uncomplicated quantum idea, in addition to for educational researchers exploring electromagnetism, particle physics, and wave mechanics and for specialists within the box of optical waveguide and built-in optics.
Prof. Zhuangqi Cao is a Professor of Physics at Shanghai Jiao Tong college, China.
Dr. Cheng Yin is a instructor at Jiangsu Key Laboratory of energy Transmission and Distribution gear know-how, Hohai collage, China.
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Extra resources for Advances in One-Dimensional Wave Mechanics: Towards A Unified Classical View
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But as the potential becomes complex, the method will be more and more useful and important. References 1. M. Born, E. Wolf, Principles of Optics [M] (Cambridge University Press, Cambridge, 1978) 2. A. Yariv, Quantum Electronics [M], 2nd edn. (Wiley, New York, 1975) 26 2 Analytical Transfer Matrix Method 3. Z. Cao, Y. Jiang, Q. Shen, X. Dou, Y. Chen, Exact analytical method for planar optical waveguides with arbitrary index profile [J]. J. Opt. Soc. Am. A 16, 2209 (1999) 4. P. Su, Z. Cao, K. Chen, X.
R þ o r 0 ð3:59Þ In the classical allowed region of infinite r, the two linearly independent solutions should be transformed into the following WKB waves: Z 1 1 ψ 0, 1 ðr Þ ¼ D0, 1 pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ cos h r p0 ð r Þ 1 0 0 ϕ p0 r dr À 0, 1 , 2 ð3:60Þ where the undetermined D0, D1 are amplitude-related coefficients and ϕ0, ϕ1 are phase related. The general waves can be constructed via these solutions. At the limit of r ! þ1 ψ ðr Þ % 1 pﬃﬃﬃﬃﬃ ½expðÀiκr Þ þ Rr expðiκr Þ, hk ð3:61Þ which includes the left-traveling incident plane wave and right-traveling reflected plane wave; Rr denotes the reflection coefficient to be derived.