February 22, 2017

Advances in One-Dimensional Wave Mechanics: Towards A by Zhuangqi Cao, Cheng Yin

By Zhuangqi Cao, Cheng Yin

Advances in One-Dimensional Wave Mechanics presents a complete description of the movement of microscopic debris in one-dimensional, arbitrary-shaped potentials according to the analogy among Quantum Mechanics and Electromagnetism. using a deeper figuring out of the wave nature of subject, this ebook introduces the concept that of the scattered sub-waves and a sequence of recent analytical effects utilizing the Analytical move Matrix (ATM) procedure. This paintings could be important for graduate scholars majoring in physics, almost always in simple quantum conception, 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 collage, China.

Dr. Cheng Yin is a instructor at Jiangsu Key Laboratory of energy Transmission and Distribution apparatus expertise, Hohai collage, China.

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58) based on the modified WKB waves. If we consider an incident electron wave packet, Z ð3:69Þ ψ ðr Þ ¼ Aðkr Þψ kr ðr Þdkr , where the coefficients A(kr) are real and the incident part of the electron wave function is ψ kr ¼ eikr rÀiEt=h . For a sufficiently smooth and narrow band, the stationary phase approximation can be used, and the phase time and group delay of the transmitted and reflected waves are τt ¼ h ∂ϕt ðkr Þ , ∂E τr ¼ h ∂ϕr ðkr Þ , ∂E ð3:70Þ respectively. Based on the phase time definition, Prof.

71) is strictly limited. 44 3 Semiclassical Approximation In conclusion, this chapter introduced the semiclassical approximation theory, which aims to provide the readers some basic concepts, so they will have the ability to compare the semiclassical approximation and the transfer matrix method for themselves. Some comments in advance: all the WKB approximation is based on the WKB waves, which confirms that the wave vector of the matter wave (momentum of the particle) at each point is determined by the particle energy pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E and the potential strength at this point, that is, κ ðxÞ ¼ 2m½E À V ðxފ=h.

This principle states that the quantum physics gives the same answer as the classical physics when the quantum number describing systems becomes large. It is Bohr correspondence principle that established the bridge between the classical mechanics and the early quantum theory [1–3]. Also based on this principle, Heisenberg established his matrix theory. In the early development of the quantum mechanics, semiclassical approximation provides a theoretical basis for the angular momentum quantization [4].

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