The physics of quantum mechanics:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2014
|
| Ausgabe: | 1. ed. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027217649&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027217649&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | 1. publ. by Capella Archive in 2008 |
| Umfang: | XIII, 392 S. graph. Darst. |
| ISBN: | 0199688567 9780199688562 0199688575 9780199688579 |
Internformat
MARC
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| 100 | 1 | |a Binney, James |d 1950- |e Verfasser |0 (DE-588)171978153 |4 aut | |
| 245 | 1 | 0 | |a The physics of quantum mechanics |c James Binney ; David Skinner |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2014 | |
| 300 | |a XIII, 392 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a 1. publ. by Capella Archive in 2008 | ||
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| 700 | 1 | |a Skinner, David |e Verfasser |0 (DE-588)1047877236 |4 aut | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0202 PHY 020f 2015 A 5012 |
|---|---|
| DE-BY-TUM_katkey | 2132847 |
| DE-BY-TUM_location | 02 |
| DE-BY-TUM_media_number | 040008068275 |
| _version_ | 1821934137443876864 |
| adam_text | Contents
Preface
xii
1
Introduction
1
1.1
Origins
2
1.2
Measurements
6
•
Measurement involves disturbance
7
> Heisenberg
microscope
7 ·
Ideal measurements
8
•
Summary
10
1.3
Probability amplitudes
11
•
Two-slit interference
12
1.4
Quantum states
14
•
Observables
14
t> Complete sets of amplitudes
14
•
Vector spaces and their duals
16 ·
The energy represen¬
tation
19 ·
Polarisation of photons
20
1.5
Summary
23
Problems
24
2
Operators, measurement and time evolution
25
2.1
Operators
25
>
Functions of operators
29 >
Commutators
29
2.2
Evolution in time
31
•
Evolution of expectation values
32
2.3
The position representation
34
•
Hamiltonian of a particle
37 ·
Wavefunction for well-
defined momentum
38 >
The uncertainty principle
39
•
Dynamics of a free particle
41 ·
Back to two-slit in¬
terference
43 ·
Generalisation to three dimensions
44
>
Probability current
45 >
The virial theorem
46
2.4
Summary
47
Problems
48
viii Contents
3
Oscillators
52
3.1
Stationary states of a harmonic oscillator
52
3.2
Dynamics of oscillators
56
•
Anharmonic oscillators
58
Problems
61
4
Transformations and
observables
66
4.1
Transforming
kets
66
•
Translating
kets
67 ·
Continuous transformations and
generators
69 ·
The rotation operator
71 ·
Discrete
transformations
72 >
The parity operator
72 >
Mirror
operators
73
4.2
Transformations of operators
74
>
The parity operator
76 >
Mirror operators
78
4.3
Symmetries and conservation laws
79
4.4
The
Heisenberg
picture
81
4.5
What is the essence of quantum mechanics?
83
Problems
85
5
Motion in step potentials
88
5.1
Square potential well
88
•
Limiting cases
91 >
Infinitely deep well
91 >
Infinitely
narrow well
92
5.2
A pair of square wells
93
•
Ammonia
96 >
The ammonia
maser
97
5.3
Scattering of free particles
99
>
The scattering cross-section
102 ·
Tunnelling through
a potential barrier
103 ·
Scattering by a classically
allowed region
104 ·
Resonant scattering
106
>
The Breit-Wigner cross-section
109
5.4
How applicable are our results?
113
5.5
Summary
115
Problems
117
6
Composite systems
123
6.1
Composite systems
124
•
Collapse of the wavefunction
128 ·
Operators for com¬
posite systems
129 ·
Development of entanglement
131
•
Einstein-Podolski-Rosen experiment
132
>
Bell s inequality
134
6.2
Quantum computing
137
Contents
їх
6.3
The density operator
144
•
Reduced density operators
148 ·
Shannon entropy
151
6.4
Thermodynamics
154
6.5
Measurement
158
Problems
162
7
Angular momentum
167
7.1
Eigenvalues of Jz and J2
168
•
Rotation spectra of diatomic molecules
171
7.2
Spin and orbital angular momentum
174
•
Orbital angular momentum
174 >
L
as the generator of
circular translations
176 >
Spectra of L2 and Lz
177
•
Spin angular momentum
177
7.3
Physics of spin
180
•
Spin-half matrices
181 ·
Spin-one matrices
182
•
The Stern—Gerlach experiment
183 >
Stern-
Gerlach experiment with spin-one atoms
186
•
Precession in a magnetic field
187 ·
The classical
limit
188
7.4
Orbital angular-momentum eigenfunctions
191
•
Orbital angular momentum and parity
196 ·
Orbital
angular momentum and kinetic energy
196 ·
Legendre
polynomials
198
7.5
Three-dimensional harmonic oscillator
199
7.6
Addition of angular momenta
205
•
Case of two spin-half systems
209 ·
Case of spin-one
and spin-half
211 ·
The classical limit
212
Problems
213
8
Hydrogen
219
8.1
Gross structure of hydrogen
220
•
Emission-line spectra
226 ·
Radial eigenfunctions
226
•
Shielding
231 ·
Expectation values for r~k
234
8.2
Fine structure and beyond
236
•
Spin—orbit coupling
236 ·
Hyperfine structure
241
Problems
243
9
Motion in a magnetic field
247
9.1
Hamiltonian for motion in a magnetic field
248
•
Classical equations of motion
248
9.2
Gauge transformations
250
•
Probability current
251
x
Contents
9.3 Landau
levels
252
•
Displacement of the gyrocentre
255
9.4
Aharonov-
Bohm
effect
257
Problems
259
10
Perturbation theory
262
10.1
Time-independent perturbations
263
•
Quadratic Stark effect
265 ·
Linear Stark effect and
degenerate perturbation theory
266 ·
Effect of an external
magnetic field
269 >
Paschen-Back effect
271 >
Zeeman
effect
271
10.2
Variational principle
273
10.3
Time-dependent perturbation theory
275
•
Fermi golden rule
276 ·
Radiative transition rates
277
•
Selection rules
282
Problems
284
11
Helium and the periodic table
290
11.1
Identical particles
290
>
Generalisation to the case of
N
identical particles
291
• Pauli
exclusion principle
292 ·
Electron pairs
293
11.2
Gross structure of helium
295
•
Gross structure from perturbation theory
296
•
Application of the variational principle to he¬
lium
298 ·
Excited states of helium
299
•
Electronic configurations and
spectroscopie
terms
302
>
Spectrum of helium
303
11.3
The periodic table
303
•
From lithium to argon
303 ·
The fourth and fifth peri¬
ods
308
Problems
309
12
Adiabatic principle
312
12.1
Derivation of the adiabatic principle
313
12.2
Application to kinetic theory
315
12.3
Application to thermodynamics
317
12.4
The compressibility of condensed matter
318
12.5
Covalent bonding
320
•
A model of a covalent bond
320 ·
Molecular dynam¬
ics
322 ·
Dissociation of molecules
323
12.6
The WKBJ approximation
324
Problems
325
Contents xi
13
Scattering theory
327
13.1
The scattering operator
328
•
Perturbative treatment of the scattering operator
330
13.2
The S-matrix
332
•
The
іє
prescription
332 ·
Expanding the S-matrix
334
•
The scattering amplitude
336
13.3
Cross-sections and scattering experiments
339
•
The optical theorem
342
13.4
Scattering electrons off hydrogen
344
13.5
Partial wave expansions
346
•
Scattering at low energy
351
13.6
Resonant scattering
353
• Breit—Wigner
resonances
356 ·
Radioactive decay
356
Problems
358
Appendices
A The laws of probability
361
В
Cartesian tensors
363
С
Fourier series and transforms
365
D
Operators in classical statistical mechanics
367
E
Lie groups and Lie algebras
369
F
The hidden symmetry of hydrogen
370
G Lorentz
covariant
equations
372
H
Thomas precession
376
I Matrix elements for
a dipole—dipole
interaction
378
J
Selection rule for
j
380
К
Restrictions on scattering potentials
381
Index
383
The book tries to convey a physical understanding of how quantum mech¬
anics describes the material world. It shows that the theory is a natural
consequence of using probability amplitudes to compute probabilities.
It stresses that stationary states are unphysical abstractions that enable us
to solve the theory s governing equation. Every opportunity is taken to show
how the classical world emerges through quantum interference between
stationary states, so students appreciate that classical physics is just
a useful approximation to a fundamentally quantum world.
The connections between
observables,
operators and transformations
are clearly explained and the standard commutation rules derived from the
properties of spacetime. A chapter covers entanglement, quantum computing,
density operators, thermodynamics and the measurement problem. Scattering
phenomena, including the origin
öf
radioactivity, are discussed in one dimen¬
sion early on and treated again and rigorously in three dimensions at the end
of the book. Hydrogen and helium are discussed in detail, and it is shown how
quantum mechanics enables us to understand the structure of the periodic
table without engaging with the complexities of many-electron atoms.
Although Dirac notation is used from the outset, the mathematical pre¬
requisites are simply vector algebra, Taylor series and the use of integrating
factors to solve differential equations. Rigorous algebraic methods are preferred
to the solution of partial differential equations/
James Binney is Head of the Rudolf Peierls Centre for Theoretical Physics
and Fellow of Merton College at the University of Oxford.
David Skinner is a Lecturer in the Department of Applied Mathematics
and Theoretical Physics at the University of Cambridge.
|
| any_adam_object | 1 |
| author | Binney, James 1950- Skinner, David |
| author_GND | (DE-588)171978153 (DE-588)1047877236 |
| author_facet | Binney, James 1950- Skinner, David |
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| building | Verbundindex |
| bvnumber | BV041771667 |
| classification_rvk | UK 1000 |
| classification_tum | PHY 020f |
| ctrlnum | (OCoLC)884360067 (DE-599)GBV770083226 |
| discipline | Physik |
| edition | 1. ed. |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV041771667 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:54:42Z |
| institution | BVB |
| isbn | 0199688567 9780199688562 0199688575 9780199688579 |
| language | English |
| lccn | 2013940021 |
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| owner_facet | DE-703 DE-20 DE-11 DE-91G DE-BY-TUM DE-19 DE-BY-UBM |
| physical | XIII, 392 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spellingShingle | Binney, James 1950- Skinner, David The physics of quantum mechanics Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4123623-3 |
| title | The physics of quantum mechanics |
| title_auth | The physics of quantum mechanics |
| title_exact_search | The physics of quantum mechanics |
| title_full | The physics of quantum mechanics James Binney ; David Skinner |
| title_fullStr | The physics of quantum mechanics James Binney ; David Skinner |
| title_full_unstemmed | The physics of quantum mechanics James Binney ; David Skinner |
| title_short | The physics of quantum mechanics |
| title_sort | the physics of quantum mechanics |
| topic | Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Quantenmechanik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027217649&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027217649&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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