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E-raamat: Advances in One-Dimensional Wave Mechanics: Towards A Unified Classical View

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  • Formaat: PDF+DRM
  • Ilmumisaeg: 16-Jan-2014
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783642408915
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Advances in One-Dimensional Wave Mechanics: Towards A Unified Classical ViewSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 16-Jan-2014
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783642408915
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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.

Prof. Zhuangqi Cao is a Professor of Physics at Shanghai Jiao Tong University, China.

Dr. Cheng Yin is a teacher at Jiangsu Key Laboratory of Power Transmission and Distribution Equipment Technology, Hohai University, China.



This book examines the motion of microscopic particles in one-dimensional, arbitrary-shaped potentials based on the analogy between Quantum Mechanics and Electromagnetism. Covers scattered sub-waves and new results using the Analytical Transfer Matrix method.

Arvustused

From the book reviews:

The motion of microscopic particles in one-dimensional, arbitrary-shaped potentials is studied in this book by using the analogy between the quantum mechanics and the electromagnetism theory. The book is of interest for graduate students learning quantum theory and for researchers in electromagnetism, and in particular in the field of optical waveguide and integrated optics. (Gheorghe Zet, zbMATH, Vol. 1297, 2014)

1 Analogy Between Quantum Mechanics and Optics
1(14)
1.1 Wave Equation
2(3)
1.1.1 One-Dimensional Scalar Wave Equation
2(2)
1.1.2 One-Dimensional Stationary Schrodinger Equation
4(1)
1.2 Optical Waveguide and Quantum Well
5(3)
1.2.1 Asymmetric Optical Waveguide
6(1)
1.2.2 Asymmetric Square Potential Well
7(1)
1.3 Tunneling Effect
8(4)
1.3.1 Optical Energy Coupling Structure
9(1)
1.3.2 Barrier Tunneling
10(2)
1.4 Square-Law Distribution
12(3)
1.4.1 Optical Waveguide with Square-Law-Distributed Refractive Index
12(1)
1.4.2 Harmonic Oscillator
13(1)
References
14(1)
2 Analytical Transfer Matrix Method
15(12)
2.1 Basic Characteristics of the Transfer Matrix
16(8)
2.1.1 Establish a Transfer Matrix
16(3)
2.1.2 Basic Characteristics of the Transfer Matrix
19(5)
2.2 Solving Simple One-Dimensional Problems
24(3)
2.2.1 Asymmetric Rectangular Potential Well
24(1)
2.2.2 Tunneling Coefficient of Rectangular Barrier
25(1)
References
25(2)
3 Semiclassical Approximation
27(20)
3.1 WKB Wave Function
28(5)
3.2 Semiclassical Limit
33(1)
3.3 Connection Formulas at Turning Points
34(3)
3.4 Application of the WKB Approximation
37(10)
3.4.1 Bound State in a Potential Well
37(2)
3.4.2 Barrier Tunneling
39(2)
3.4.3 Some Related Topics
41(3)
References
44(3)
4 Exact Quantization Condition via Analytical Transfer Matrix Method
47(28)
4.1 Double-Well Potentials
48(3)
4.2 One-Dimensional Potential of Arbitrary Shape
51(11)
4.2.1 Analysis of One-Dimensional Problems via Transfer Matrix
51(5)
4.2.2 Phase Shift at Classical Turning Points
56(1)
4.2.3 Phase Contribution of Scattered Subwaves
57(1)
4.2.4 Eigenvalue Equation
58(2)
4.2.5 The Calculation of the Wave Function
60(1)
4.2.6 Accidental Event of the WKB Approximation
61(1)
4.3 Energy Splitting in Symmetric Double-Well Potentials
62(4)
4.3.1 One-Dimensional Square Double-Well Potential
62(2)
4.3.2 One-Dimensional Symmetric Double-Well Potentials
64(2)
4.4 Example of the Lennard-Jones Potential
66(3)
4.5 Direct Derivation of the Exact Quantization Condition
69(6)
References
72(3)
5 Barrier Tunneling
75(22)
5.1 One-Dimensional Arbitrary Continuous Barrier
76(8)
5.1.1 ATM Reflection Coefficient with a Constant Effective Mass
76(5)
5.1.2 The Case of m = 1 and m = 2
81(2)
5.1.3 Continuous Potential at the Reference Point
83(1)
5.2 Compared with WKB Approximation
84(4)
5.2.1 Barrier with Adjacent Wells
84(2)
5.2.2 Band-Pass Filter Based on a Gaussian-Modulated Superlattice
86(2)
5.3 One-Dimensional Arbitrary Continuous Barrier with Position-Dependent Effective Mass
88(9)
5.3.1 Derivation of Reflection Coefficient
88(5)
5.3.2 The Semiconductor Single Barrier Structure
93(1)
5.3.3 Semiconductor Double-Barrier Structure with Nonlinear Potential
94(1)
References
95(2)
6 The Scattered Subwaves
97
6.1 Basic Concept
98(2)
6.1.1 Conceptual Difference of the Wave Vector
98(1)
6.1.2 Numerical Comparison of the Total Wavenumber and the Main Wavenumber
99(1)
6.2 The Scattered Subwaves and the Quantum Reflection
100(9)
6.2.1 Research Progress in Quantum Reflection
101(1)
6.2.2 Explanation by the ATM Method
102(7)
6.3 Time Issue in One-Dimensional Scattering
109(20)
6.3.1 Barrier Tunneling Time and the Hartman Effect
109(3)
6.3.2 Analogy Between Electron Tunneling and Electromagnetic Tunneling
112(2)
6.3.3 Reinterpretation of the Phase Time
114(2)
6.3.4 Generalized Expression for Reflection Time
116(6)
6.3.5 General Transmission Time
122(4)
6.3.6 Scattered Subwayes and the Hartman Effect
126(3)
6.4 Scattered Subwaves and the Supersymmetric Quantum Mechanics
129
6.4.1 Brief Introduction of Supersymmetric Quantum Mechanics
130(2)
6.4.2 SWKB Approximation
132(2)
6.4.3 Consideration of the Scattered Subwaves
134(7)
6.4.4 Why Is SWKB Quantization Condition Exact?
141(3)
References
144
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