Fundamentals of quantum mechanics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Taylor & Francis
2007
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 433 S. graph. Darst. |
| ISBN: | 1584887338 9781584887324 |
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MARC
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| 020 | |a 9781584887324 |c hbk. |9 978-1-584-88732-4 | ||
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| 100 | 1 | |a Erkoç, Şakir |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fundamentals of quantum mechanics |c Şakir Erkoç |
| 264 | 1 | |a New York, NY [u.a.] |b Taylor & Francis |c 2007 | |
| 300 | |a 433 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Record in the Search Index
| _version_ | 1804138999599595520 |
|---|---|
| adam_text | Contents
Preface
Part—I: Fundamentals and One—Dimensional Systems
1
1
Historical Experiments and Theories
3
1.1
Dates of important discoveries and events
........... 3
1.2
Blackbody
radiation
....................... 3
1.3
Photoelectric effect
....................... 9
1.4
Quantum theory of spectra
................... 13
1.5
The Compton effect
....................... 18
1.6
Matter waves, the
de Broglie
hypothesis
............ 19
1.7
The Davisson-
Germer
experiment
............... 21
1.8
Heisenberg s uncertainty principle
............... 22
1.9
Difference between particles and waves
............ 24
1.10
Interpretation of the wavefunction
............... 26
1.11
Worked examples
........................ 27
1.12
Problems
............................. 30
2
Axiomatic Structure of Quantum Mechanics
31
2.1
The necessity of quantum theory
................ 31
2.2
Function spaces
......................... 31
2.3
Postulates of quantum mechanics
............... 34
2.4
The
Kronecker
delta and the Dirac delta function
...... 46
2.5
Dirac notation
.......................... 49
2.6
Worked examples
........................ 51
2.7
Problems
............................. 56
3
Observables
and Superposition
57
3.1
Free particle
........................... 57
3.2
Particle in a box
......................... 59
3.3
Ensemble average
........................ 64
3.4
Hubert space interpretation
.................. 66
3.5
The initial square wave
..................... 67
3.6
Particle beam
.......................... 69
3.7
Superposition and uncertainty
................. 70
3.8
Degeneracy of states
....................... 72
3.9
Commutators and uncertainty
................. 74
3.10
Worked examples
........................ 75
3.11
Problems
............................. 77
4
Time Development and Conservation Theorems
79
4.1
Time development of state functions. The discrete case
... 79
4.2
The continuous case. Wave packets
.............. 81
4.3
Particle beam
.......................... 83
4.4
Gaussian wave packet
...................... 84
4.5
Free Particle propagator
.................... 85
4.6
The limiting cases of the Gaussian wave packets
....... 87
4.7
Time development of expectation values
............ 89
4.8
Conservation of energy and momentum
............ 91
4.9
Conservation of parity
...................... 93
4.10
Worked examples
........................ 96
4.11
Problems
............................. 99
5
Bound and Unbound States in One—Dimension
101
5.1
One-dimensional
Schrödinger
equation
............ 101
5.2
The simple harmonic oscillator
................. 103
5.3
Unbound states
......................... 117
5.4
One-dimensional barrier problems
............... 122
5.5
The finite potential well
..................... 134
5.6
Worked examples
........................ 146
5.7
Problems
............................. 152
Part—II: Three-Dimensional Systems
153
6 N
Particle Systems
155
6.1
The
Schrödinger
equation for N- particle systems
....... 155
6.2
Identical particles
........................ 158
G.3 The
Pauli
principle:
fermions
and bosons
........... 160
6.4
Worked examples
........................ 165
6.5
Problems
............................. 168
7
The
Schrödinger
Equation in Three—Dimensions
169
7.1
The two body systems
..................... 169
7.2
Separation of variables in the two-body systems
....... 170
7.3
Rotational
invariance
...................... 173
7.4
The
Schrödinger
equation for noncentral potentials
..... 174
7.5
Worked examples
........................ 177
7.6
Problems
............................. 180
8
Angular
Momentum
181
8.1
Commutation relations
..................... 181
8.2
Raising and lowering operators
................. 182
8.3 Eigensolutions
of angular momentum operators
........ 183
8.4
Kinetic energy and angular momentum
............ 190
8.5
Worked examples
........................ 191
8.6
Problems
............................. 196
9
The Radial Equation for Free and Bound Particles
197
9.1
The radial
Schrödinger
equation
................ 197
9.2
The free particle
......................... 200
9.3
Three-dimensional square well potential
............ 203
9.4
The hydrogen atom
....................... 207
9.5
The Spectra of hydrogenic atoms
................ 213
9.6
The Virial Theorem
....................... 219
9.7
Worked examples
........................ 221
9.8
Problems
............................. 229
10
Interaction of Electrons with Electromagnetic Field
231
10.1
Maxwell s equations and gauge transformations
....... 231
10.2
Motion of a free electron in a uniform magnetic field
..... 233
10.3
Motion of a bound electron in a uniform magnetic field
. . . 236
10.4
The principle of gauge
invariance
and flux quantization
. . . 239
10.5
Worked examples
........................ 244
10.6
Problems
............................. 248
11
Matrix Representations
249
11.1
Matrix representations of wave functions and operators
. . . 249
11.2
Matrix algebra
.......................... 250
11.2.1
Some definitions
..................... 251
11.3
Types of matrix representations
................ 253
11.4
Harmonic oscillator in matrix representations
......... 257
11.5
Matrix representations of angular momentum operators
. . . 262
11.6
Worked examples
........................ 266
11.7
Problems
............................. 269
12
Spin and the Addition of Angular Momenta
271
12.1
Systems with spin one-half
................... 271
12.2
The addition of angular momenta
............... 281
12.3
Worked examples
........................ 285
12.4
Problems
............................. 288
Part—III: Approximation Methods and Scattering Theory
289
13
Time-Independent Perturbation Theory
291
13.1
Nondegenerate perturbation theory
.............. 291
13.2
Degenerate perturbation theory
................ 294
13.3
Worked examples
........................ 299
13.4
Problems
............................. 304
14
The Variational Method
305
14.1
The variational principle
.................... 305
14.2
Linear variation functions
.................... 307
14.3
Worked examples
........................ 308
14.4
Problems
............................. 312
15
The WKB Approximation
313
15.1
Turning points
.......................... 313
15.2
The connection formulas
.................... 315
15.3
The WKB approximation to a potential well
......... 317
15.4
The WKB approximation to a potential barrier
....... 318
15.5
Worked examples
........................ 321
15.6
Problems
............................. 324
16
Time-Dependent Perturbation Theory
325
16.1
Time-dependent
Schrödinger
equation
............. 325
16.2
Time dependent perturbation approximations
........ 327
16.3
Sinusoidal perturbations
.................... 328
16.4
Emission and absorption of radiation
............. 330
16.5
Incoherent perturbations
.................... 332
16.6
Selection rules
.......................... 335
16.7
Worked examples
........................ 337
16.8
Problems
............................. 340
17
The Adiabatic Approximation
341
17.1
The adiabatic processes
..................... 341
17.2
The adiabatic theorem
..................... 342
17.3
Nonholonomic processes
..................... 344
17.4
Experimental evidences of nonholonomic processes
...... 346
17.5
Worked examples
........................ 349
17.6
Problems
............................. 351
18
Path Integration Method
353
18.1
An approximation to time- evolution for a free particle
. . . 353
18.2
Path integral evaluation of the free particle propagator
. . . 356
18.3
Equivalence to the
Schrödinger
equation
........... 359
18.4
Worked examples
........................ 361
18.5
Problems
............................. 364
19
Scattering Theory
365
19.1
Classical scattering theory
................... 365
19.2
Center-of-mass and laboratory frames
............ 368
19.3
Quantum scattering theory
................... 370
19.4
The method of partial waves (low-energy case)
........ 372
19.5
Expansion of a plane wave into spherical waves
........ 374
19.6
Expansion of the scattering amplitude
............. 376
19.7
Scattering from a delta potential
................ 378
19.8
Scattering from a square-well potential
............ 379
19.9
Scattering from a hard sphere
................. 381
19.10
Scattering of identical particles
................ 382
19.11
Energy dependence and resonance scattering
......... 384
19.12
The Lippman-Schwinger equation (high-energy case)
.... 388
19.13
The Greens function for the scattering problem
....... 389
19.14
Born approximation
...................... 391
19.15
Inelastic Scattering
....................... 395
19.16
Worked examples
........................ 399
19.17
Problems
............................. 406
Bibliography and References
407
Appendix
411
Index
415
|
| any_adam_object | 1 |
| author | Erkoç, Şakir |
| author_facet | Erkoç, Şakir |
| author_role | aut |
| author_sort | Erkoç, Şakir |
| author_variant | ş e şe |
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| bvnumber | BV023801507 |
| classification_rvk | UK 1000 |
| ctrlnum | (OCoLC)836323210 (DE-599)BVBBV023801507 |
| 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 |
| format | Book |
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| spelling | Erkoç, Şakir Verfasser aut Fundamentals of quantum mechanics Şakir Erkoç New York, NY [u.a.] Taylor & Francis 2007 433 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantenmechanik (DE-588)4047989-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Quantenmechanik (DE-588)4047989-4 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017443706&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4047989-4 (DE-588)4123623-3 |
| title | Fundamentals of quantum mechanics |
| title_auth | Fundamentals of quantum mechanics |
| title_exact_search | Fundamentals of quantum mechanics |
| title_full | Fundamentals of quantum mechanics Şakir Erkoç |
| title_fullStr | Fundamentals of quantum mechanics Şakir Erkoç |
| title_full_unstemmed | Fundamentals of quantum mechanics Şakir Erkoç |
| title_short | Fundamentals of quantum mechanics |
| title_sort | fundamentals of quantum mechanics |
| topic | Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Quantenmechanik Lehrbuch |
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