Principles of quantum mechanics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2008
|
| Edition: | 2. ed., [Nachdr.; corr. print.] |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 676 S. graph. Darst. |
| ISBN: | 9780306447907 0306447908 |
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MARC
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| 245 | 1 | 0 | |a Principles of quantum mechanics |c R. Shankar |
| 250 | |a 2. ed., [Nachdr.; corr. print.] | ||
| 264 | 1 | |a New York, NY |b Springer |c 2008 | |
| 300 | |a XVIII, 676 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804137695212994560 |
|---|---|
| adam_text | Contents
1.
Mathematical Introduction
................... 1
1.1.
Linear Vector Spaces
:
Basics
................ 1
1.2.
Inner Product Spaces
................... 7
1.3.
Dual Spaces and the Dirac Notation
............ 11
1.4.
Subspaces
........................ 17
1.5.
Linear Operators
..................... 18
1.6.
Matrix Elements of Linear Operators
............ 20
1.7.
Active and Passive Transformations
............. 29
1.8.
The Eigenvalue Problem
.................. 30
1.9.
Functions of Operators and Related Concepts
........ 54
1.10.
Generalization to Infinite Dimensions
............ 57
2.
Review of Classical Mechanics
.................. 75
2.1.
The Principle of Least Action and Lagrangian Mechanics
... 78
2.2.
The Electromagnetic Lagrangian
.............. 83
2.3.
The Two-Body Problem
.................. 85
2.4.
How Smart Is a Particle?
................. 86
2.5.
The Hamiltonian Formalism
................ 86
2.6.
The Electromagnetic Force in the Hamiltonian Scheme
.... 90
2.7.
Cyclic Coordinates,
Poisson
Brackets, and Canonical
Transformations
..................... 91
2.8.
Symmetries and Their Consequences
............ 98
3.
All Is Not Well with Classical Mechanics
............. 107
3.1.
Particles and Waves in Classical Physics
........... 107
3.2.
An Experiment with Waves and Particles (Classical)
..... 108
3.3.
The Double-Slit Experiment with Light
........... 110
3.4.
Matter Waves
(de
Broglie Waves)
............. 112
3.5.
Conclusions
....................... 112
xv
xvi 4.
The Postulates
—
a General Discussion
.............. 115
CONTENTS
4.1.
The Postulates
...................... 115
4.2.
Discussion of Postulates I—III
............... 116
4.3.
The
Schrödinger
Equation (Dotting Your
/ s
and
Crossing your
и ѕ)
.................... 143
5.
Simple Problems in One Dimension
................ 151
5.1.
The Free Particle
..................... 151
5.2.
The Particle in a Box
................... 157
5.3.
The Continuity Equation for Probability
........... 164
5.4.
The Single-Step Potential: a Problem in Scattering
...... 167
5.5.
The Double-Slit Experiment
................ 175
5.6.
Some Theorems
..................... 176
6.
The Classical Limit
...................... 179
7.
The Harmonic Oscillator
.................... 185
7.1.
Why Study the Harmonic Oscillator?
............ 185
7.2.
Review of the Classical Oscillator
.............. 188
7.3.
Quantization of the Oscillator (Coordinate Basis)
....... 189
7.4.
The Oscillator in the Energy Basis
............. 202
7.5.
Passage from the Energy Basis to the X Basis
........ 216
8.
The Path Integral Formulation of Quantum Theory
......... 223
8.1.
The Path Integral Recipe
................. 223
8.2.
Analysis of the Recipe
.................. 224
8.3.
An Approximation to U(t) for the Free Particle
....... 225
8.4.
Path Integral Evaluation of the Free-Particle Propagator
.... 226
8.5.
Equivalence to the
Schrödinger
Equation
.......... 229
8.6.
Potentials of the Form V=a + bx+cx2 + dx+exx
....... 231
9.
The
Heisenberg
Uncertainty Relations
............... 237
9.1.
Introduction
....................... 237
9.2.
Derivation of the Uncertainty Relations
........... 237
9.3.
The Minimum Uncertainty Packet
............. 239
9.4.
Applications of the Uncertainty Principle
.......... 241
9.5.
The Energy-Time Uncertainty Relation
........... 245
10.
Systems with ./V Degrees of Freedom
............... 247
10.1. N
Particles in One Dimension
............... 247
10.2.
More Particles in More Dimensions
............ 259
10.3.
Identical Particles
.................... 260
11.
Symmetries and Their Consequences
............... 279 xvii
11.1.
Overview
........................ 279
contents
11.2.
Translational
Invariance
in Quantum Theory
........ 279
11.3.
Time Translational
Invariance
............... 294
11.4.
Parity
Invariance
.................... 297
11.5.
Time-Reversal Symmetry
................. 301
12.
Rotational
Invariance
and Angular Momentum
........... 305
12.1.
Translations in Two Dimensions
.............. 305
12.2.
Rotations in Two Dimensions
............... 306
12.3.
The Eigenvalue Problem of L·
............... 313
12.4.
Angular Momentum in Three Dimensions
......... 318
12.5.
The Eigenvalue Problem of
L
2 and L-
........... 321
12.6.
Solution of Rotationally Invariant Problems
........ 339
13.
The Hydrogen Atom
...................... 353
13.1.
The Eigenvalue Problem
................. 353
13.2.
The Degeneracy of the Hydrogen Spectrum
......... 359
13.3.
Numerical Estimates and Comparison with Experiment
.... 361
13.4.
Multielectron Atoms and the Periodic Table
........ 369
14.
Spin
............................. 373
14.1.
Introduction
...................... 373
14.2.
What is the Nature of Spin?
............... 373
14.3.
Kinematics of Spin
................... 374
14.4.
Spin Dynamics
..................... 385
14.5.
Return of Orbital Degrees of Freedom
........... 397
15.
Addition of Angular Momenta
.................. 403
15.1.
A Simple Example
.................... 403
15.2.
The General Problem
.................. 408
15.3.
Irreducible Tensor Operators
............... 416
15.4.
Explanation of Some Accidental Degeneracies
....... 421
16.
Variational and WKB Methods
................. 429
16.1.
The Variational Method
................. 429
16.2.
The Wentzel-Kramers-Brillouin Method
.......... 435
17.
Time-Independent Perturbation Theory
451
17.1.
The Formalism
.....................
451
17.2.
Some Examples
..................... 454
17.3.
Degenerate Perturbation Theory
.............. 464
xviii 18.
Time-Dependent Perturbation Theory
............... 473
contents
18.1.
The Problem
...................... 473
18.2.
First-Order Perturbation Theory
.............. 474
18.3.
Higher Orders in Perturbation Theory
........... 484
18.4.
A General Discussion of Electromagnetic Interactions
.... 492
18.5.
Interaction of Atoms with Electromagnetic Radiation
.... 499
19.
Scattering Theory
....................... 523
19.1.
Introduction
...................... 523
19.2.
Recapitulation of One-Dimensional Scattering and Overview
. 524
19.3.
The Born Approximation (Time-Dependent Description)
. . . 529
19.4.
Born Again (The Time-Independent Approximation)
..... 534
19.5.
The Partial Wave Expansion
............... 545
19.6.
Two-Particle Scattering
.................. 555
20.
The Dirac Equation
...................... 563
20.1.
The Free-Particle Dirac Equation
............. 563
20.2.
Electromagnetic Interaction of the Dirac Particle
...... 566
20.3.
More on Relativistic Quantum Mechanics
......... 574
21.
Path Integrals—II
....................... 581
21.1.
Derivation of the Path Integral
.............. 582
21.2.
Imaginary Time Formalism
................ 613
21.3.
Spin and Fermion Path Integrals
............. 636
21.4.
Summary
........................ 652
Appendix
............................. 655
A.I. Matrix Inversion
..................... 655
A.2. Gaussian Integrals
.................... 659
A.3. Complex Numbers
.................... 660
A.4. The is Prescription
.................... 661
Answers to Selected Exercises
................... 665
Table of Constants
........................ 669
Index
............................... 671
|
| adam_txt |
Contents
1.
Mathematical Introduction
. 1
1.1.
Linear Vector Spaces
:
Basics
. 1
1.2.
Inner Product Spaces
. 7
1.3.
Dual Spaces and the Dirac Notation
. 11
1.4.
Subspaces
. 17
1.5.
Linear Operators
. 18
1.6.
Matrix Elements of Linear Operators
. 20
1.7.
Active and Passive Transformations
. 29
1.8.
The Eigenvalue Problem
. 30
1.9.
Functions of Operators and Related Concepts
. 54
1.10.
Generalization to Infinite Dimensions
. 57
2.
Review of Classical Mechanics
. 75
2.1.
The Principle of Least Action and Lagrangian Mechanics
. 78
2.2.
The Electromagnetic Lagrangian
. 83
2.3.
The Two-Body Problem
. 85
2.4.
How Smart Is a Particle?
. 86
2.5.
The Hamiltonian Formalism
. 86
2.6.
The Electromagnetic Force in the Hamiltonian Scheme
. 90
2.7.
Cyclic Coordinates,
Poisson
Brackets, and Canonical
Transformations
. 91
2.8.
Symmetries and Their Consequences
. 98
3.
All Is Not Well with Classical Mechanics
. 107
3.1.
Particles and Waves in Classical Physics
. 107
3.2.
An Experiment with Waves and Particles (Classical)
. 108
3.3.
The Double-Slit Experiment with Light
. 110
3.4.
Matter Waves
(de
Broglie Waves)
. 112
3.5.
Conclusions
. 112
xv
xvi 4.
The Postulates
—
a General Discussion
. 115
CONTENTS
4.1.
The Postulates
. 115
4.2.
Discussion of Postulates I—III
. 116
4.3.
The
Schrödinger
Equation (Dotting Your
/'s
and
Crossing your
и'ѕ)
. 143
5.
Simple Problems in One Dimension
. 151
5.1.
The Free Particle
. 151
5.2.
The Particle in a Box
. 157
5.3.
The Continuity Equation for Probability
. 164
5.4.
The Single-Step Potential: a Problem in Scattering
. 167
5.5.
The Double-Slit Experiment
. 175
5.6.
Some Theorems
. 176
6.
The Classical Limit
. 179
7.
The Harmonic Oscillator
. 185
7.1.
Why Study the Harmonic Oscillator?
. 185
7.2.
Review of the Classical Oscillator
. 188
7.3.
Quantization of the Oscillator (Coordinate Basis)
. 189
7.4.
The Oscillator in the Energy Basis
. 202
7.5.
Passage from the Energy Basis to the X Basis
. 216
8.
The Path Integral Formulation of Quantum Theory
. 223
8.1.
The Path Integral Recipe
. 223
8.2.
Analysis of the Recipe
. 224
8.3.
An Approximation to U(t) for the Free Particle
. 225
8.4.
Path Integral Evaluation of the Free-Particle Propagator
. 226
8.5.
Equivalence to the
Schrödinger
Equation
. 229
8.6.
Potentials of the Form V=a + bx+cx2 + dx+exx
. 231
9.
The
Heisenberg
Uncertainty Relations
. 237
9.1.
Introduction
. 237
9.2.
Derivation of the Uncertainty Relations
. 237
9.3.
The Minimum Uncertainty Packet
. 239
9.4.
Applications of the Uncertainty Principle
. 241
9.5.
The Energy-Time Uncertainty Relation
. 245
10.
Systems with ./V Degrees of Freedom
. 247
10.1. N
Particles in One Dimension
. 247
10.2.
More Particles in More Dimensions
. 259
10.3.
Identical Particles
. 260
11.
Symmetries and Their Consequences
. 279 xvii
11.1.
Overview
. 279
contents
11.2.
Translational
Invariance
in Quantum Theory
. 279
11.3.
Time Translational
Invariance
. 294
11.4.
Parity
Invariance
. 297
11.5.
Time-Reversal Symmetry
. 301
12.
Rotational
Invariance
and Angular Momentum
. 305
12.1.
Translations in Two Dimensions
. 305
12.2.
Rotations in Two Dimensions
. 306
12.3.
The Eigenvalue Problem of L·
. 313
12.4.
Angular Momentum in Three Dimensions
. 318
12.5.
The Eigenvalue Problem of
L
2 and L-
. 321
12.6.
Solution of Rotationally Invariant Problems
. 339
13.
The Hydrogen Atom
. 353
13.1.
The Eigenvalue Problem
. 353
13.2.
The Degeneracy of the Hydrogen Spectrum
. 359
13.3.
Numerical Estimates and Comparison with Experiment
. 361
13.4.
Multielectron Atoms and the Periodic Table
. 369
14.
Spin
. 373
14.1.
Introduction
. 373
14.2.
What is the Nature of Spin?
. 373
14.3.
Kinematics of Spin
. 374
14.4.
Spin Dynamics
. 385
14.5.
Return of Orbital Degrees of Freedom
. 397
15.
Addition of Angular Momenta
. 403
15.1.
A Simple Example
. 403
15.2.
The General Problem
. 408
15.3.
Irreducible Tensor Operators
. 416
15.4.
Explanation of Some "Accidental" Degeneracies
. 421
16.
Variational and WKB Methods
. 429
16.1.
The Variational Method
. 429
16.2.
The Wentzel-Kramers-Brillouin Method
. 435
17.
Time-Independent Perturbation Theory
451
17.1.
The Formalism
.
451
17.2.
Some Examples
. 454
17.3.
Degenerate Perturbation Theory
. 464
xviii 18.
Time-Dependent Perturbation Theory
. 473
contents
18.1.
The Problem
. 473
18.2.
First-Order Perturbation Theory
. 474
18.3.
Higher Orders in Perturbation Theory
. 484
18.4.
A General Discussion of Electromagnetic Interactions
. 492
18.5.
Interaction of Atoms with Electromagnetic Radiation
. 499
19.
Scattering Theory
. 523
19.1.
Introduction
. 523
19.2.
Recapitulation of One-Dimensional Scattering and Overview
. 524
19.3.
The Born Approximation (Time-Dependent Description)
. . . 529
19.4.
Born Again (The Time-Independent Approximation)
. 534
19.5.
The Partial Wave Expansion
. 545
19.6.
Two-Particle Scattering
. 555
20.
The Dirac Equation
. 563
20.1.
The Free-Particle Dirac Equation
. 563
20.2.
Electromagnetic Interaction of the Dirac Particle
. 566
20.3.
More on Relativistic Quantum Mechanics
. 574
21.
Path Integrals—II
. 581
21.1.
Derivation of the Path Integral
. 582
21.2.
Imaginary Time Formalism
. 613
21.3.
Spin and Fermion Path Integrals
. 636
21.4.
Summary
. 652
Appendix
. 655
A.I. Matrix Inversion
. 655
A.2. Gaussian Integrals
. 659
A.3. Complex Numbers
. 660
A.4. The is Prescription
. 661
Answers to Selected Exercises
. 665
Table of Constants
. 669
Index
. 671 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Shankar, Ramamurti |
| author_facet | Shankar, Ramamurti |
| author_role | aut |
| author_sort | Shankar, Ramamurti |
| author_variant | r s rs |
| building | Verbundindex |
| bvnumber | BV023341924 |
| classification_rvk | UK 1000 |
| classification_tum | PHY 020f |
| ctrlnum | (OCoLC)234171831 (DE-599)BVBBV023341924 |
| 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., [Nachdr.; corr. print.] |
| format | Book |
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| id | DE-604.BV023341924 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:01:54Z |
| indexdate | 2024-07-09T21:16:23Z |
| institution | BVB |
| isbn | 9780306447907 0306447908 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016525680 |
| oclc_num | 234171831 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-384 DE-83 DE-19 DE-BY-UBM DE-91G DE-BY-TUM |
| owner_facet | DE-355 DE-BY-UBR DE-384 DE-83 DE-19 DE-BY-UBM DE-91G DE-BY-TUM |
| physical | XVIII, 676 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| spelling | Shankar, Ramamurti Verfasser aut Principles of quantum mechanics R. Shankar 2. ed., [Nachdr.; corr. print.] New York, NY Springer 2008 XVIII, 676 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantentheorie Quantum theory Schrödinger-Gleichung (DE-588)4053332-3 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Vektorrechnung (DE-588)4062471-7 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s DE-604 Mathematik (DE-588)4037944-9 s 1\p DE-604 Schrödinger-Gleichung (DE-588)4053332-3 s 2\p DE-604 Quantentheorie (DE-588)4047992-4 s 3\p DE-604 Vektorrechnung (DE-588)4062471-7 s 4\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016525680&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Shankar, Ramamurti Principles of quantum mechanics Quantentheorie Quantum theory Schrödinger-Gleichung (DE-588)4053332-3 gnd Quantentheorie (DE-588)4047992-4 gnd Quantenmechanik (DE-588)4047989-4 gnd Mathematik (DE-588)4037944-9 gnd Vektorrechnung (DE-588)4062471-7 gnd |
| subject_GND | (DE-588)4053332-3 (DE-588)4047992-4 (DE-588)4047989-4 (DE-588)4037944-9 (DE-588)4062471-7 |
| title | Principles of quantum mechanics |
| title_auth | Principles of quantum mechanics |
| title_exact_search | Principles of quantum mechanics |
| title_exact_search_txtP | Principles of quantum mechanics |
| title_full | Principles of quantum mechanics R. Shankar |
| title_fullStr | Principles of quantum mechanics R. Shankar |
| title_full_unstemmed | Principles of quantum mechanics R. Shankar |
| title_short | Principles of quantum mechanics |
| title_sort | principles of quantum mechanics |
| topic | Quantentheorie Quantum theory Schrödinger-Gleichung (DE-588)4053332-3 gnd Quantentheorie (DE-588)4047992-4 gnd Quantenmechanik (DE-588)4047989-4 gnd Mathematik (DE-588)4037944-9 gnd Vektorrechnung (DE-588)4062471-7 gnd |
| topic_facet | Quantentheorie Quantum theory Schrödinger-Gleichung Quantenmechanik Mathematik Vektorrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016525680&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT shankarramamurti principlesofquantummechanics |