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E-raamat: Introduction to Quantum Mechanics 2 - Wave-Corpuscle, Quantization & Schroedinger's Equation: Wave-Corpuscle, Quantization and Schrodinger's Equation [Wiley Online]

(University of Thiès, Senegal)
  • Formaat: 304 pages
  • Ilmumisaeg: 14-Feb-2020
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 1119694930
  • ISBN-13: 9781119694939
Teised raamatud teemal:
  • Wiley Online
  • Hind: 174,45 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
Introduction to Quantum Mechanics 2 - Wave-Corpuscle, Quantization & Schroedinger's Equation: Wave-Corpuscle, Quantization and Schrodinger's EquationSuurem pilt
  • Formaat: 304 pages
  • Ilmumisaeg: 14-Feb-2020
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 1119694930
  • ISBN-13: 9781119694939
Teised raamatud teemal:
Wiley Online e-raamatudRohkem infot Wiley Online kohta
Raamatu kodulehekülg: https://onlinelibrary.wiley.com/doi/book/10.1002/9781119694939
Quantum mechanics is the foundation of modern technology, due to its innumerable applications in physics, chemistry and even biology.





This second volume studies Schrödingers equation and its applications in the study of wells, steps and potential barriers. It examines the properties of orthonormal bases in the space of square-summable wave functions and Dirac notations in the space of states.





This book has a special focus on the notions of the linear operators, the Hermitian operators, observables, Hermitian conjugation, commutators and the representation of kets, bras and operators in the space of states. The eigenvalue equation, the characteristic equation and the evolution equation of the mean value of an observable are introduced. The book goes on to investigate the study of conservative systems through the time evolution operator and Ehrenfests theorem.





Finally, this second volume is completed by the introduction of the notions of quantum wire, quantum wells of semiconductor materials and quantum dots in the appendices.
Foreword xi
Preface xiii
Chapter 1 Schrodinger's Equation and its Applications
1(126)
1.1 Physical state and physical quantity
2(1)
1.1.1 Dynamic state of a particle
2(1)
1.1.2 Physical quantities associated with a particle
3(1)
1.2 Square-summable wave function
3(2)
1.2.1 Definition, superposition principle
3(1)
1.2.2 Properties
4(1)
1.3 Operator
5(6)
1.3.1 Definition of an operator, examples
5(1)
1.3.2 Hermitian operator
5(2)
1.3.3 Linear observable operator
7(1)
1.3.4 Correspondence principle, Hamiltonian
8(3)
1.4 Evolution of physical systems
11(4)
1.4.1 Time-dependent Schrodinger equation
11(1)
1.4.2 Stationary Schrodinger equation
12(2)
1.4.3 Evolution operator
14(1)
1.5 Properties of Schrodinger's equation
15(4)
1.5.1 Determinism in the evolution of physical systems
15(1)
1.5.2 Superposition principle
15(1)
1.5.3 Probability current density
16(3)
1.6 Applications of Schrodinger's equation
19(26)
1.6.1 Infinitely deep potential well
19(5)
1.6.2 Potential step
24(8)
1.6.3 Potential barrier, tunnel effect
32(7)
1.6.4 Quantum dot
39(3)
1.6.5 Ground state energy of hydrogen-like systems
42(3)
1.7 Exercises
45(20)
1.7.1 Exercise 1 - Probability current density
45(1)
1.7.2 Exercise 2 - Heisenberg's spatial uncertainty relations
46(1)
1.7.3 Exercise 3 - Finite-depth potential step
47(1)
1.7.4 Exercise 4 - Multistep potential
48(2)
1.7.5 Exercise 5 - Particle confined in a rectangular potential
50(1)
1.7.6 Exercise 6 - Square potential well: unbound states
51(1)
1.7.7 Exercise 7 - Square potential well: bound states
52(1)
1.7.8 Exercise 8 - Infinitely deep rectangular potential well
53(1)
1.7.9 Exercise 9 - Metal assimilated to a potential well, cold emission
54(2)
1.7.10 Exercise 10 - Ground state energy of the harmonic oscillator
56(1)
1.7.11 Exercise 11 - Quantized energy of the harmonic oscillator
57(1)
1.7.12 Exercise 12 - HC1 molecule assimilated to a linear oscillator
58(1)
1.7.13 Exercise 13 - Quantized energy of hydrogen-like systems
59(1)
1.7.14 Exercise 14 - Line integral of the probability current density vector, Bohr's magneton
60(2)
1.7.15 Exercise 15 - The Schrodinger equation in the presence of a magnetic field, Zeeman-Lorentz triplet
62(1)
1.7.16 Exercise 16 - Deduction of the stationary Schrodinger equation from De Broglie relation
63(2)
1.8 Solutions
65(62)
1.8.1 Solution 1 - Probability current density
65(2)
1.8.2 Solution 2 - Heisenberg's spatial uncertainty relations
67(3)
1.8.3 Solution 3 - Finite-depth potential step
70(4)
1.8.4 Solution 4 - Multistep potential
74(3)
1.8.5 Solution 5 - Particle confined in a rectangular potential
77(4)
1.8.6 Solution 6 - Square potential well: unbound states
81(5)
1.8.7 Solution 7 - Square potential well: bound states
86(8)
1.8.8 Solution 8 - Infinitely deep rectangular potential well
94(5)
1.8.9 Solution 9 - Metal assimilated to a potential well, cold emission
99(2)
1.8.10 Solution 10 - Ground state energy of the harmonic oscillator
101(3)
1.8.11 Solution 11 - Quantized energy of the harmonic oscillator
104(4)
1.8.12 Solution 12 - HC1 molecule assimilated to a linear oscillator
108(4)
1.8.13 Solution 13 - Quantized energy of hydrogen-like systems
112(4)
1.8.14 Solution 14 - Line integral of the probability current density vector, Bohr's magneton
116(3)
1.8.15 Solution 15 - The Schrodinger equation in the presence of a magnetic field, Zeeman-Lorentz triplet
119(3)
1.8.16 Solution 16 - Deduction of the Schrodinger equation from De Broglie relation
122(5)
Chapter 2 Hermitian Operator, Dirac's Notations
127(48)
2.1 Orthonormal bases in the space of square-summable wave functions
129(3)
2.1.1 Subspace of square-summable wave functions
129(1)
2.1.2 Definition of discrete orthonormal bases
129(1)
2.1.3 Component and norm of a wave function
130(1)
2.1.4 Closing relation
131(1)
2.2 Space of states, Dirac's notations
132(3)
2.2.1 Definition
132(1)
2.2.2 Ket vector, bra vector
133(1)
2.2.3 Properties of the scalar product
134(1)
2.2.4 Discrete orthonormal bases, ket component
134(1)
2.3 Hermitian operators
135(6)
2.3.1 Linear operator, matrix element
135(1)
2.3.2 Projection operator on a ket and projection operator on a sub-space
136(3)
2.3.3 Self-adjoint operator, Hermitian conjugation
139(1)
2.3.4 Operator functions
140(1)
2.4 Commutator algebra
141(8)
2.4.1 Poisson brackets
141(3)
2.4.2 Commutation of operator functions
144(4)
2.4.3 Trace of an operator
148(1)
2.5 Exercises
149(4)
2.5.1 Exercise 1 - Properties of commutators
149(1)
2.5.2 Exercise 2 - Trace of an operator
150(1)
2.5.3 Exercise 3 - Function of operators
150(1)
2.5.4 Exercise 4 - Infinitesimal unitary operator
151(1)
2.5.5 Exercise 5 - Properties of Pauli matrices
151(1)
2.5.6 Exercise 6 - Density operator
152(1)
2.5.7 Exercise 7 - Evolution operator
152(1)
2.5.8 Exercise 8 - Orbital angular momentum operator
153(1)
2.6 Solutions
153(22)
2.6.1 Solution 1 - Properties of commutators
153(4)
2.6.2 Solution 2 - Trace of an operator
157(2)
2.6.3 Solution 3 - Function of operators
159(2)
2.6.4 Solution 4 - Infinitesimal unitary operator
161(2)
2.6.5 Solution 5 - Properties of Pauli matrices
163(4)
2.6.6 Solution 6 - Density operator
167(1)
2.6.7 Solution 7 - Evolution operator
168(4)
2.6.8 Solution 8 - Orbital angular momentum operator
172(3)
Chapter 3 Eigenvalues and Eigenvectors of an Observable
175(82)
3.1 Representation
176(4)
3.1.1 Definition
176(1)
3.1.2 Representation of kets and bras
177(1)
3.1.3 Representation of operators
177(2)
3.1.4 Hermitian matrix
179(1)
3.2 Eigenvalues equation, mean value
180(9)
3.2.1 Definitions, degeneracy
180(3)
3.2.2 Characteristic equation
183(3)
3.2.3 Properties of eigenvectors and eigenvalues of a Hermitian operator
186(1)
3.2.4 Evolution of the mean value of an observable
187(2)
3.2.5 Complete set of commuting observables
189(1)
3.3 Conservative systems
189(5)
3.3.1 Definition
189(1)
3.3.2 Integration of the Schrodinger equation
190(2)
3.3.3 Ehrenfest's theorem
192(2)
3.4 Exercises
194(11)
3.4.1 Exercise 1 - Pauli matrices, eigenvalues and eigenvectors
194(1)
3.4.2 Exercise 2 - Observables associated with the spin
194(2)
3.4.3 Exercise 3 - Evolution of a 1/2 spin in a magnetic field: CSCO, Larmor precession
196(1)
3.4.4 Exercise 4 - Eigenvalue of the squared angular momentum operator
197(1)
3.4.5 Exercise 5 - Constant of motion, good quantum numbers
198(1)
3.4.6 Exercise 6 - Evolution of the mean values of the operators associated with position and linear momentum
198(1)
3.4.7 Exercise 7-Particle subjected to various potentials
199(1)
3.4.8 Exercise 8 - Oscillating molecular dipole, root mean square deviation
199(1)
3.4.9 Exercise 9 - Infinite potential well, time-energy uncertainty relation
200(2)
3.4.10 Exercise 10 - Study of a conservative system
202(1)
3.4.11 Exercise 11 - Evolution of the density operator
203(1)
3.4.12 Exercise 12 - Evolution of a 1/2 spin in a magnetic field
203(2)
3.5 Solutions
205(52)
3.5.1 Solution 1 - Pauli matrices, eigenvalues and eigenvectors
205(3)
3.5.2 Solution 2 - Observables associated with the spin
208(4)
3.5.3 Solution 3 - Evolution of a 1/2 spin in a magnetic field: CSCO, Larmor precession
212(2)
3.5.4 Solution 4 - Eigenvalue of the square angular momentum operator
214(6)
3.5.5 Solution 5 - Constant of motion, good quantum numbers
220(1)
3.5.6 Solution 6 - Evolution of the mean values of the operators associated with position and linear momentum
221(5)
3.5.7 Solution 7 - Particle subjected to various potentials
226(2)
3.5.8 Solution 8 - Oscillating molecular dipole, root mean square deviation
228(5)
3.5.9 Solution 9 - Infinite potential well, time-energy uncertainty relation
233(9)
3.5.10 Solution 10 - Study of a conservative system
242(7)
3.5.11 Solution 11 - Evolution of the density operator
249(3)
3.5.12 Solution 12 - Evolution of a 1/2 spin in a magnetic field
252(5)
Appendix 1 257(8)
Appendix 2 265(4)
Appendix 3 269(6)
References 275(2)
Index 277
Ibrahima Sakho is a Doctor of Physical Science, and works at the science and technology training and research unit at the University of Thiès (Senegal). On-site, he teaches quantum mechanics, atomic and nuclear physics, radiation–matter interaction, and environmental chemistry.
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