Title Advances in one-dimensional wave mechanics : towards a unified classical view / Zhuangqi Cao, Cheng Yin

Published Heidelberg : Springer, 2014

Table of Contents
1.	Analogy Between Quantum Mechanics and Optics					1
1.1.	Wave Equation					2
1.1.1.	One-Dimensional Scalar Wave Equation					2
1.1.2.	One-Dimensional Stationary Schrodinger Equation					4
1.2.	Optical Waveguide and Quantum Well					5
1.2.1.	Asymmetric Optical Waveguide					6
1.2.2.	Asymmetric Square Potential Well					7
1.3.	Tunneling Effect					8
1.3.1.	Optical Energy Coupling Structure					9
1.3.2.	Barrier Tunneling					10
1.4.	Square-Law Distribution					12
1.4.1.	Optical Waveguide with Square-Law-Distributed Refractive Index					12
1.4.2.	Harmonic Oscillator					13
	References					14
2.	Analytical Transfer Matrix Method					15
2.1.	Basic Characteristics of the Transfer Matrix					16
2.1.1.	Establish a Transfer Matrix					16
2.1.2.	Basic Characteristics of the Transfer Matrix					19
2.2.	Solving Simple One-Dimensional Problems					24
2.2.1.	Asymmetric Rectangular Potential Well					24
2.2.2.	Tunneling Coefficient of Rectangular Barrier					25
	References					25
3.	Semiclassical Approximation					27
3.1.	WKB Wave Function					28
3.2.	Semiclassical Limit					33
3.3.	Connection Formulas at Turning Points					34
3.4.	Application of the WKB Approximation					37
3.4.1.	Bound State in a Potential Well					37
3.4.2.	Barrier Tunneling					39
3.4.3.	Some Related Topics					41
	References					44
4.	Exact Quantization Condition via Analytical Transfer Matrix Method					47
4.1.	Double-Well Potentials					48
4.2.	One-Dimensional Potential of Arbitrary Shape					51
4.2.1.	Analysis of One-Dimensional Problems via Transfer Matrix					51
4.2.2.	Phase Shift at Classical Turning Points					56
4.2.3.	Phase Contribution of Scattered Subwaves					57
4.2.4.	Eigenvalue Equation					58
4.2.5.	The Calculation of the Wave Function					60
4.2.6.	Accidental Event of the WKB Approximation					61
4.3.	Energy Splitting in Symmetric Double-Well Potentials					62
4.3.1.	One-Dimensional Square Double-Well Potential					62
4.3.2.	One-Dimensional Symmetric Double-Well Potentials					64
4.4.	Example of the Lennard-Jones Potential					66
4.5.	Direct Derivation of the Exact Quantization Condition					69
	References					72
5.	Barrier Tunneling					75
5.1.	One-Dimensional Arbitrary Continuous Barrier					76
5.1.1.	ATM Reflection Coefficient with a Constant Effective Mass					76
5.1.2.	The Case of m = 1 and m = 2					81
5.1.3.	Continuous Potential at the Reference Point					83
5.2.	Compared with WKB Approximation					84
5.2.1.	Barrier with Adjacent Wells					84
5.2.2.	Band-Pass Filter Based on a Gaussian-Modulated Superlattice					86
5.3.	One-Dimensional Arbitrary Continuous Barrier with Position-Dependent Effective Mass					88
5.3.1.	Derivation of Reflection Coefficient					88
5.3.2.	The Semiconductor Single Barrier Structure					93
5.3.3.	Semiconductor Double-Barrier Structure with Nonlinear Potential					94
	References					95
6.	The Scattered Subwaves					97
6.1.	Basic Concept					98
6.1.1.	Conceptual Difference of the Wave Vector					98
6.1.2.	Numerical Comparison of the Total Wavenumber and the Main Wavenumber					99
6.2.	The Scattered Subwaves and the Quantum Reflection					100
6.2.1.	Research Progress in Quantum Reflection					101
6.2.2.	Explanation by the ATM Method					102
6.3.	Time Issue in One-Dimensional Scattering					109
6.3.1.	Barrier Tunneling Time and the Hartman Effect					109
6.3.2.	Analogy Between Electron Tunneling and Electromagnetic Tunneling					112
6.3.3.	Reinterpretation of the Phase Time					114
6.3.4.	Generalized Expression for Reflection Time					116
6.3.5.	General Transmission Time					122
6.3.6.	Scattered Subwayes and the Hartman Effect					126
6.4.	Scattered Subwaves and the Supersymmetric Quantum Mechanics					129
6.4.1.	Brief Introduction of Supersymmetric Quantum Mechanics					130
6.4.2.	SWKB Approximation					132
6.4.3.	Consideration of the Scattered Subwaves					134
6.4.4.	Why Is SWKB Quantization Condition Exact?					141
	References					144

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Description 1 online resource (ix, 145 pages) : illustrations (some color) Contents Analogy between Quantum Mechanics and Optics -- Analytical Transfer Matrix method -- Semiclassical Approximation -- Exact Quantization Condition via Analytical Transfer Matrix method -- Barrier Tunneling -- The Scattered Subwaves Summary Advances in One-Dimensional Wave Mechanics provides a comprehensive description of the motion of microscopic particles in one-dimensional, arbitrary-shaped potentials based on the analogy between Quantum Mechanics and Electromagnetism. Utilizing a deeper understanding of the wave nature of matter, this book introduces the concept of the scattered sub-waves and a series of new analytical results using the Analytical Transfer Matrix (ATM) method. This work will be useful for graduate students majoring in physics, mainly in basic quantum theory, as well as for academic researchers exploring electromagnetism, particle physics, and wave mechanics and for experts in the field of optical waveguide and integrated optics Bibliography Includes bibliographical references Notes English Online resource; title from PDF title page (SpringerLink, viewed January 20, 2014) In Springer eBooks Subject Wave mechanics. SCIENCE -- Energy. SCIENCE -- Mechanics -- General. SCIENCE -- Physics -- General. Physique. Astronomie. Wave mechanics Genre/Form Conference papers and proceedings Form Electronic book Author Yin, Cheng, author ISBN 9783642408915 3642408915 3642408907 9783642408908 9787313101471 7313101473

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