Download e-book for iPad: Advances in One-Dimensional Wave Mechanics: Towards A by Zhuangqi Cao, Cheng Yin

By Zhuangqi Cao, Cheng Yin

ISBN-10: 3642408907

ISBN-13: 9783642408908

ISBN-10: 3642408915

ISBN-13: 9783642408915

Advances in One-Dimensional Wave Mechanics presents a finished description of the movement of microscopic debris in one-dimensional, arbitrary-shaped potentials in accordance with the analogy among Quantum Mechanics and Electromagnetism. using a deeper knowing of the wave nature of subject, this publication introduces the idea that of the scattered sub-waves and a chain of latest analytical effects utilizing the Analytical move Matrix (ATM) approach. This paintings should be beneficial for graduate scholars majoring in physics, frequently in simple quantum thought, in addition to for tutorial 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 college, China.

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C and D are coefficients to be determined. The above two equations are known as the first order of the approximated WKB wave function, which holds when the potential V(x) varies very slowly, that is, in the range of the de Broglie wavelength of the particle [13]. The careful reader may note that neither Eq. 17) is pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi applicable in the vicinity of the turning points, since p and 2m½V ðxÞ À EŠ approach zero. Or the wavelength tends to infinity near the classical turning points and the requirement Eq.

In this chapter, both the bounded states in a potential well and the one-dimensional scattering are discussed based on the WKB approximation. Keywords WKB approximation • Semiclassical limit • Connection formulas • Classical turning point • Quantization condition • Quantum reflection In the first chapter, we discussed the similarity between the optics and quantum mechanics. Although in the early nineteenth century, Irish mathematician W. R. Hamilton presented a theory of a single function known as Hamilton’s principal function, which brings together mechanics and optics, the similarity between quantum mechanics and classical electromagnetic field theory has not brought enough attention after the establishment of quantum mechanics.

Ann. der 4. A. Sommerfeld, U Physik 50, 385 (1916) 5. J. Zeng, Quantum Mechanics, vol. I [M] (Science Press, Beijing, 2007) 6. G. Wentzel, A generalisation of the quantum constraints for the purposes of the wave mechanics [J]. Z. Physik 38, 518 (1926) 7. A. Kramers, Wave mechanics and half-integral quantization [J]. Z. Physik 39, 828 (1926) 8. L. R. Hebd, The undulatory mechanics of Schro¨dinger [J]. Acad. Sci. 183, 24 (1926) 9. H. Friedrich, J. Trost, Nonintegral Maslov indices [J]. Phys. Rev.

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

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