Applied quantum mechanics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2006
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 558 S. Ill., graph. Darst. |
| ISBN: | 0521860962 9780521860963 |
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MARC
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| 100 | 1 | |a Levi, Anthony F. J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Applied quantum mechanics |c A. F. J. Levi |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2006 | |
| 300 | |a XVI, 558 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Quantum theory | |
| 650 | 4 | |a Quantum theory |x Industrial applications | |
| 650 | 0 | 7 | |a Quantenmechanik |0 (DE-588)4047989-4 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-014800024 | ||
Record in the Search Index
| _version_ | 1804135358111154176 |
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| adam_text | Contents
Preface
to the first edition page
xiii
Preface to the second edition
xv
MATLAB®
programs
xvi
1
Introduction
1
1.1
Motivation
1
1.2
Classical mechanics
4
1.2.1
Introduction
4
1.2.2
The one-dimensional simple harmonic oscillator
7
1.2.3
Harmonic oscillation of a diatomic molecule
10
1.2.4
The monatomic linear chain
13
1.2.5
The diatomic linear chain
15
1.3
Classical
electromagnetism
18
1.3.1
Electrostatics
18
1.3.2
Electrodynamics
24
1.4
Example exercises
39
1.5
Problems
53
2
Toward quantum mechanics
57
2.1
Introduction
57
2.1.1
Diffraction and interference of light
58
2.1.2
Black-body radiation and evidence for quantization of light
62
2.1.3
Photoelectric effect and the photon particle
64
2.1.4
Secure quantum communication
66
2.1.5
The link between quantization of photons and other particles
70
2.1.6
Diffraction and interference of electrons
71
2.1.7
When is a particle a wave?
72
2.2
The
Schrödinger
wave equation
73
2.2.1
The wave function description of an electron in free space
79
2.2.2
The electron wave packet and dispersion
80
2.2.3
The hydrogen atom
83
2.2.4
Periodic table of elements
89
2.2.5
Crystal structure
93
2.2.6
Electronic properties of bulk semiconductors and heterostructures
96
vii
CONTENTS
2.3
Example exercises
103
2.4
Problems
114
3
Using the
Schrödinger
wave equation
117
3.1
Introduction
117
3.1.1
The effect of discontinuity in the wave function and its slope
118
3.2
Wave function normalization and completeness
121
3.3
Inversion symmetry in the potential
122
3.3.1
One-dimensional rectangular potential well with infinite
barrier energy
123
3.4
Numerical solution of the
Schrödinger
equation
126
3.5
Current flow
128
3.5.1
Current in a rectangular potential well with infinite barrier
energy
129
3.5.2
Current flow due to a traveling wave
131
3.6
Degeneracy as a consequence of symmetry
131
3.6.1
Bound states in three dimensions and degeneracy of eigenvalues
131
3.7
Symmetric finite-barrier potential
133
3.7.1
Calculation of bound states in a symmetric finite-barrier
potential
135
3.8
Transmission and reflection of unbound states
137
3.8.1
Scattering from a potential step when
/я, =т2
138
3.8.2
Scattering from a potential step when m{
φ
m2
140
3.8.3
Probability current density for scattering at a step
141
3.8.4
Impedance matching for unity transmission across a
potential step
142
3.9
Particle tunneling
145
3.9.1
Electron tunneling limit to reduction in size of CMOS
transistors
149
3.10
The nonequilibrium electron transistor
150
3.11
Example exercises
155
3.12
Problems
168
4
Electron propagation
171
4.1
Introduction
171
4.2
The propagation matrix method
172
4.3
Program to calculate transmission probability
177
4.4
Time-reversal symmetry
178
4.5
Current conservation and the propagation matrix
180
4.6
The rectangular potential barrier
182
4.6.1
Transmission probability for a rectangular potential barrier
182
4.6.2
Transmission as a function of energy
185
4.6.3
Transmission resonances
186
4.7
Resonant tunneling
188
4.7.1
Heterostructure bipolar transistor with resonant tunnel-barrier
190
4.7.2
Resonant tunneling between two quantum wells
192
vm
CONTENTS
4.8
The potential barrier in the delta function limit
197
4.9
Energy bands in a periodic potential
199
4.9.1
Bloch s Theorem
200
4.9.2
The propagation matrix applied to a periodic potential
201
4.9.3
The tight binding approximation
207
4.9.4
Crystal momentum and effective electron mass
209
4.10
Other engineering applications
213
4.11
The WKB approximation
214
4.11.1
Tunneling through a high-energy barrier of finite width
215
4.12
Example exercises
217
4.13
Problems
234
5
Eigenstates and operators
238
5.1
Introduction
238
5.1.1
The postulates of quantum mechanics
238
5.2
One-particle wave function space
239
5.3
Properties of linear operators
240
5.3.1
Product of operators
241
5.3.2
Properties of Hermitian operators
241
5.3.3
Normalization of eigenfunctions
243
5.3.4
Completeness of eigenfunctions
243
5.3.5
Commutator algebra
244
5.4
Dirac notation
245
5.5
Measurement of real numbers
246
5.5.1
Expectation value of an operator
247
5.5.2
Time dependence of expectation value
248
5.5.3
Uncertainty of expectation value
249
5.5.4
The generalized uncertainty relation
253
5.6
The no cloning theorem
255
5.7
Density of states
256
5.7.1
Density of electron states
256
5.7.2
Calculating density of states from a dispersion relation
263
5.7.3
Density of photon states
264
5.8
Example exercises
266
5.9
Problems
277
6
The harmonic oscillator
280
6.1
The harmonic oscillator potential
280
6.2
Creation and annihilation operators
282
6.2.1
The ground state of the harmonic oscillator
284
6.2.2
Excited states of the harmonic oscillator and normalization
of eigenstates
287
6.3
The harmonic oscillator wave functions
291
6.3.1
The classical turning point of the harmonic oscillator
295
6.4
Time dependence
298
6.4.1
The superposition operator
300
ix
CONTENTS
6.4.2
Measurement of a superposition state
300
6.4.3
Time dependence of creation and annihilation operators
301
6.5
Quantization of electromagnetic fields
305
6.5.1
Laser light
306
6.5.2
Quantization of an electrical resonator
306
6.6
Quantization of lattice vibrations
307
6.7
Quantization of mechanical vibrations
308
6.8
Example exercises
309
6.9
Problems
323
7
Fermions
and bosons
326
7.1
Introduction
326
7.1.1
The symmetry of indistinguishable particles
327
7.2
Fermi-Dirac distribution and chemical potential
334
7.2.1
Writing a computer program to calculate the chemical potential
337
7.2.2
Writing a computer program to plot the Fermi-Dirac distribution
338
7.2.3
Fermi-Dirac distribution function and thermal equilibrium
statistics
339
7.3
The Bose-Einstein distribution function
342
7.4
Example exercises
343
7.5
Problems
351
8
Time-dependent perturbation
353
8.1
Introduction
353
8.1.1
An abrupt change in potential
354
8.1.2
Time-dependent change in potential
356
8.2
First-order time-dependent perturbation
359
8.2.1
Charged particle in a harmonic potential
360
8.3
Fermi s golden rule
363
8.4
Elastic scattering from ionized impurities
366
8.4.1
The coulomb potential
369
8.4.2
Linear screening of the coulomb potential
375
8.5
Photon emission due to electronic transitions
384
8.5.1
Density of optical modes in three-dimensions
384
8.5.2
Light intensity
385
8.5.3
Background photon energy density at thermal equilibrium
385
8.5.4
Fermi s golden rale for stimulated optical transitions
385
8.5.5
The Einstein
Л
and
S
coefficients
387
8.6
Example exercises
393
8.7
Problems
407
9
The semiconductor laser
412
9.1
Introduction
412
9.2
Spontaneous and stimulated emission
413
9.2.1
Absorption and its relation to spontaneous emission
416
CONTENTS
9.3
Optical transitions using Fermi s golden rale
419
9.3.1
Optical gain in the presence of electron scattering
420
9.4
Designing a laser diode
422
9.4.1
The optical cavity
422
9.4.2
Mirror loss and photon lifetime
428
9.4.3
The Fabry-Perot laser diode
429
9.4.4
Semiconductor laser diode rate equations
430
9.5
Numerical method of solving rate equations
434
9.5.1
The Runge-Kutta method
435
9.5.2
Large-signal transient response
437
9.5.3
Cavity formation
438
9.6
Noise in laser diode light emission
440
9.7
Why our model works
443
9.8
Example exercises
443
9.9
Problems
449
10
Time-independent perturbation
450
10.1
Introduction
450
10.2
Time-independent
nondegenerate
perturbation
451
10.2.1
The first-order correction
452
10.2.2
The second-order correction
453
10.2.3
Harmonic oscillator subject to perturbing potential in
χ
456
10.2.4
Harmonic oscillator subject to perturbing potential in x2
458
10.2.5
Harmonic oscillator subject to perturbing potential in x3
459
10.3
Time-independent degenerate perturbation
461
10.3.1
A two-fold degeneracy split by time-independent
perturbation
462
10.3.2
Matrix method
462
10.3.3
The two-dimensional harmonic oscillator subject to
perturbation in xy
465
10.3.4
Perturbation of two-dimensional potential with infinite
barrier energy
467
10.4
Example exercises
471
10.5
Problems
482
11
Angular momentum and the hydrogenic atom
485
11.1
Angular momentum
485
11.1.1
Classical angular momentum
485
11.2
The angular momentum operator
487
11.2.1
Eigenvalues of angular momentum operators Lz and L2
489
11.2.2
Geometrical representation
491
11.2.3
Spherical coordinates and spherical harmonics
492
11.2.4
The rigid rotator
498
11.3
The hydrogen atom
499
11.3.1
Eigenstates and eigenvalues of the hydrogen atom
500
11.3.2
Hydrogenic atom wave functions
508
xi
CONTENTS
11.3.3
Electromagnetic radiation
509
11.3.4
Fine structure
of the hydrogen atom and electron spin
515
11.4
Hybridization
516
11.5
Example exercises
517
11.6
Problems
529
Appendix A Physical values
532
Appendix
В
Coordinates, trigonometry, and mensuration
537
Appendix
С
Expansions, differentiation, integrals, and mathematical relations
540
Appendix
D
Matrices and determinants
546
Appendix
E
Vector calculus and Maxwell
s
equations
548
Appendix
F
The Greek alphabet
551
Index
552
xii
|
| adam_txt |
Contents
Preface
to the first edition page
xiii
Preface to the second edition
xv
MATLAB®
programs
xvi
1
Introduction
1
1.1
Motivation
1
1.2
Classical mechanics
4
1.2.1
Introduction
4
1.2.2
The one-dimensional simple harmonic oscillator
7
1.2.3
Harmonic oscillation of a diatomic molecule
10
1.2.4
The monatomic linear chain
13
1.2.5
The diatomic linear chain
15
1.3
Classical
electromagnetism
18
1.3.1
Electrostatics
18
1.3.2
Electrodynamics
24
1.4
Example exercises
39
1.5
Problems
53
2
Toward quantum mechanics
57
2.1
Introduction
57
2.1.1
Diffraction and interference of light
58
2.1.2
Black-body radiation and evidence for quantization of light
62
2.1.3
Photoelectric effect and the photon particle
64
2.1.4
Secure quantum communication
66
2.1.5
The link between quantization of photons and other particles
70
2.1.6
Diffraction and interference of electrons
71
2.1.7
When is a particle a wave?
72
2.2
The
Schrödinger
wave equation
73
2.2.1
The wave function description of an electron in free space
79
2.2.2
The electron wave packet and dispersion
80
2.2.3
The hydrogen atom
83
2.2.4
Periodic table of elements
89
2.2.5
Crystal structure
93
2.2.6
Electronic properties of bulk semiconductors and heterostructures
96
vii
CONTENTS
2.3
Example exercises
103
2.4
Problems
114
3
Using the
Schrödinger
wave equation
117
3.1
Introduction
117
3.1.1
The effect of discontinuity in the wave function and its slope
118
3.2
Wave function normalization and completeness
121
3.3
Inversion symmetry in the potential
122
3.3.1
One-dimensional rectangular potential well with infinite
barrier energy
123
3.4
Numerical solution of the
Schrödinger
equation
126
3.5
Current flow
128
3.5.1
Current in a rectangular potential well with infinite barrier
energy
129
3.5.2
Current flow due to a traveling wave
131
3.6
Degeneracy as a consequence of symmetry
131
3.6.1
Bound states in three dimensions and degeneracy of eigenvalues
131
3.7
Symmetric finite-barrier potential
133
3.7.1
Calculation of bound states in a symmetric finite-barrier
potential
135
3.8
Transmission and reflection of unbound states
137
3.8.1
Scattering from a potential step when
/я, =т2
138
3.8.2
Scattering from a potential step when m{
φ
m2
140
3.8.3
Probability current density for scattering at a step
141
3.8.4
Impedance matching for unity transmission across a
potential step
142
3.9
Particle tunneling
145
3.9.1
Electron tunneling limit to reduction in size of CMOS
transistors
149
3.10
The nonequilibrium electron transistor
150
3.11
Example exercises
155
3.12
Problems
168
4
Electron propagation
171
4.1
Introduction
171
4.2
The propagation matrix method
172
4.3
Program to calculate transmission probability
177
4.4
Time-reversal symmetry
178
4.5
Current conservation and the propagation matrix
180
4.6
The rectangular potential barrier
182
4.6.1
Transmission probability for a rectangular potential barrier
182
4.6.2
Transmission as a function of energy
185
4.6.3
Transmission resonances
186
4.7
Resonant tunneling
188
4.7.1
Heterostructure bipolar transistor with resonant tunnel-barrier
190
4.7.2
Resonant tunneling between two quantum wells
192
vm
CONTENTS
4.8
The potential barrier in the delta function limit
197
4.9
Energy bands in a periodic potential
199
4.9.1
Bloch's Theorem
200
4.9.2
The propagation matrix applied to a periodic potential
201
4.9.3
The tight binding approximation
207
4.9.4
Crystal momentum and effective electron mass
209
4.10
Other engineering applications
213
4.11
The WKB approximation
214
4.11.1
Tunneling through a high-energy barrier of finite width
215
4.12
Example exercises
217
4.13
Problems
234
5
Eigenstates and operators
238
5.1
Introduction
238
5.1.1
The postulates of quantum mechanics
238
5.2
One-particle wave function space
239
5.3
Properties of linear operators
240
5.3.1
Product of operators
241
5.3.2
Properties of Hermitian operators
241
5.3.3
Normalization of eigenfunctions
243
5.3.4
Completeness of eigenfunctions
243
5.3.5
Commutator algebra
244
5.4
Dirac notation
245
5.5
Measurement of real numbers
246
5.5.1
Expectation value of an operator
247
5.5.2
Time dependence of expectation value
248
5.5.3
Uncertainty of expectation value
249
5.5.4
The generalized uncertainty relation
253
5.6
The no cloning theorem
255
5.7
Density of states
256
5.7.1
Density of electron states
256
5.7.2
Calculating density of states from a dispersion relation
263
5.7.3
Density of photon states
264
5.8
Example exercises
266
5.9
Problems
277
6
The harmonic oscillator
280
6.1
The harmonic oscillator potential
280
6.2
Creation and annihilation operators
282
6.2.1
The ground state of the harmonic oscillator
284
6.2.2
Excited states of the harmonic oscillator and normalization
of eigenstates
287
6.3
The harmonic oscillator wave functions
291
6.3.1
The classical turning point of the harmonic oscillator
295
6.4
Time dependence
298
6.4.1
The superposition operator
300
ix
CONTENTS
6.4.2
Measurement of a superposition state
300
6.4.3
Time dependence of creation and annihilation operators
301
6.5
Quantization of electromagnetic fields
305
6.5.1
Laser light
306
6.5.2
Quantization of an electrical resonator
306
6.6
Quantization of lattice vibrations
307
6.7
Quantization of mechanical vibrations
308
6.8
Example exercises
309
6.9
Problems
323
7
Fermions
and bosons
326
7.1
Introduction
326
7.1.1
The symmetry of indistinguishable particles
327
7.2
Fermi-Dirac distribution and chemical potential
334
7.2.1
Writing a computer program to calculate the chemical potential
337
7.2.2
Writing a computer program to plot the Fermi-Dirac distribution
338
7.2.3
Fermi-Dirac distribution function and thermal equilibrium
statistics
339
7.3
The Bose-Einstein distribution function
342
7.4
Example exercises
343
7.5
Problems
351
8
Time-dependent perturbation
353
8.1
Introduction
353
8.1.1
An abrupt change in potential
354
8.1.2
Time-dependent change in potential
356
8.2
First-order time-dependent perturbation
359
8.2.1
Charged particle in a harmonic potential
360
8.3
Fermi's golden rule
363
8.4
Elastic scattering from ionized impurities
366
8.4.1
The coulomb potential
369
8.4.2
Linear screening of the coulomb potential
375
8.5
Photon emission due to electronic transitions
384
8.5.1
Density of optical modes in three-dimensions
384
8.5.2
Light intensity
385
8.5.3
Background photon energy density at thermal equilibrium
385
8.5.4
Fermi's golden rale for stimulated optical transitions
385
8.5.5
The Einstein
Л
and
S
coefficients
387
8.6
Example exercises
393
8.7
Problems
407
9
The semiconductor laser
412
9.1
Introduction
412
9.2
Spontaneous and stimulated emission
413
9.2.1
Absorption and its relation to spontaneous emission
416
CONTENTS
9.3
Optical transitions using Fermi's golden rale
419
9.3.1
Optical gain in the presence of electron scattering
420
9.4
Designing a laser diode
422
9.4.1
The optical cavity
422
9.4.2
Mirror loss and photon lifetime
428
9.4.3
The Fabry-Perot laser diode
429
9.4.4
Semiconductor laser diode rate equations
430
9.5
Numerical method of solving rate equations
434
9.5.1
The Runge-Kutta method
435
9.5.2
Large-signal transient response
437
9.5.3
Cavity formation
438
9.6
Noise in laser diode light emission
440
9.7
Why our model works
443
9.8
Example exercises
443
9.9
Problems
449
10
Time-independent perturbation
450
10.1
Introduction
450
10.2
Time-independent
nondegenerate
perturbation
451
10.2.1
The first-order correction
452
10.2.2
The second-order correction
453
10.2.3
Harmonic oscillator subject to perturbing potential in
χ
456
10.2.4
Harmonic oscillator subject to perturbing potential in x2
458
10.2.5
Harmonic oscillator subject to perturbing potential in x3
459
10.3
Time-independent degenerate perturbation
461
10.3.1
A two-fold degeneracy split by time-independent
perturbation
462
10.3.2
Matrix method
462
10.3.3
The two-dimensional harmonic oscillator subject to
perturbation in xy
465
10.3.4
Perturbation of two-dimensional potential with infinite
barrier energy
467
10.4
Example exercises
471
10.5
Problems
482
11
Angular momentum and the hydrogenic atom
485
11.1
Angular momentum
485
11.1.1
Classical angular momentum
485
11.2
The angular momentum operator
487
11.2.1
Eigenvalues of angular momentum operators Lz and L2
489
11.2.2
Geometrical representation
491
11.2.3
Spherical coordinates and spherical harmonics
492
11.2.4
The rigid rotator
498
11.3
The hydrogen atom
499
11.3.1
Eigenstates and eigenvalues of the hydrogen atom
500
11.3.2
Hydrogenic atom wave functions
508
xi
CONTENTS
11.3.3
Electromagnetic radiation
509
11.3.4
Fine structure
of the hydrogen atom and electron spin
515
11.4
Hybridization
516
11.5
Example exercises
517
11.6
Problems
529
Appendix A Physical values
532
Appendix
В
Coordinates, trigonometry, and mensuration
537
Appendix
С
Expansions, differentiation, integrals, and mathematical relations
540
Appendix
D
Matrices and determinants
546
Appendix
E
Vector calculus and Maxwell'
s
equations
548
Appendix
F
The Greek alphabet
551
Index
552
xii |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Levi, Anthony F. J. |
| author_facet | Levi, Anthony F. J. |
| author_role | aut |
| author_sort | Levi, Anthony F. J. |
| author_variant | a f j l afj afjl |
| building | Verbundindex |
| bvnumber | BV021584425 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.12 |
| callnumber-search | QC174.12 |
| callnumber-sort | QC 3174.12 |
| callnumber-subject | QC - Physics |
| classification_rvk | UK 1000 UK 1050 |
| classification_tum | PHY 020f |
| ctrlnum | (OCoLC)254699674 (DE-599)BVBBV021584425 |
| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
| dewey-sort | 3530.12 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV021584425 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:42:34Z |
| indexdate | 2024-07-09T20:39:14Z |
| institution | BVB |
| isbn | 0521860962 9780521860963 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014800024 |
| oclc_num | 254699674 |
| open_access_boolean | |
| owner | DE-20 DE-91G DE-BY-TUM DE-1050 DE-83 DE-355 DE-BY-UBR |
| owner_facet | DE-20 DE-91G DE-BY-TUM DE-1050 DE-83 DE-355 DE-BY-UBR |
| physical | XVI, 558 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Levi, Anthony F. J. Verfasser aut Applied quantum mechanics A. F. J. Levi 2. ed. Cambridge [u.a.] Cambridge Univ. Press 2006 XVI, 558 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantentheorie Quantum theory Quantum theory Industrial applications Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014800024&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Levi, Anthony F. J. Applied quantum mechanics Quantentheorie Quantum theory Quantum theory Industrial applications Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047989-4 |
| title | Applied quantum mechanics |
| title_auth | Applied quantum mechanics |
| title_exact_search | Applied quantum mechanics |
| title_exact_search_txtP | Applied quantum mechanics |
| title_full | Applied quantum mechanics A. F. J. Levi |
| title_fullStr | Applied quantum mechanics A. F. J. Levi |
| title_full_unstemmed | Applied quantum mechanics A. F. J. Levi |
| title_short | Applied quantum mechanics |
| title_sort | applied quantum mechanics |
| topic | Quantentheorie Quantum theory Quantum theory Industrial applications Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Quantentheorie Quantum theory Quantum theory Industrial applications Quantenmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014800024&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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