MARC details
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07756nam a2200397 i 4500 |
| 001 - CONTROL NUMBER |
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44097 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
BD-DhAAL |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20250213162241.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
130405t20132013nyua b 001 0 eng c |
| 010 ## - LIBRARY OF CONGRESS CONTROL NUMBER |
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| LC control number |
2013937175 |
| 016 7# - NATIONAL BIBLIOGRAPHIC AGENCY CONTROL NUMBER |
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| Record control number |
016488175 |
| Source |
Uk |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781461471158 (acidfree paper) |
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| International Standard Book Number |
146147115X (acidfree paper) |
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| International Standard Book Number |
9781461471165 |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(OCoLC)ocn828487961 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
BTCTA |
| Language of cataloging |
eng |
| Transcribing agency |
BTCTA |
| Description conventions |
rda |
| Modifying agency |
YDXCP |
| -- |
CSA |
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OHX |
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TXA |
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OCLCQ |
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UKMGB |
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STF |
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HEBIS |
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IQU |
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PUL |
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OCLCF |
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IXA |
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DLC |
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BD-DhAAL |
| 042 ## - AUTHENTICATION CODE |
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| Authentication code |
pcc |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QC174.12 |
| Item number |
.H346 2013 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
QA |
| Source |
lcco |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
530.12 |
| Edition number |
22 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Hall, Brian C., |
| Relator term |
author. |
| 9 (RLIN) |
21848 |
| 245 10 - TITLE STATEMENT |
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| Title |
Quantum theory for mathematicians / |
| Statement of responsibility, etc |
Brian C. Hall. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
New York : |
| Name of publisher, distributor, etc |
Springer, |
| Date of publication, distribution, etc |
2013. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xvi, 554 pages : |
| Other physical details |
illustrations ; |
| Dimensions |
24 cm |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Graduate texts in mathematics, |
| International Standard Serial Number |
0072-5285 ; |
| Volume number/sequential designation |
267 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
|---|
| Bibliography, etc |
Includes bibliographical references (pages 545-548) and index. |
| 505 00 - FORMATTED CONTENTS NOTE |
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| Title |
The experimental origins of quantum mechanics: |
| -- |
Is light a wave or a particle? ; |
| -- |
Is an electron a wave or a particle? ; |
| -- |
Schrödinger and Heisenberg ; |
| -- |
A matter of interpretation ; |
| Miscellaneous information |
Exercises -- |
| Title |
A first approach to classical mechanics: |
| -- |
Motion in R¹ ; |
| -- |
Motion in R[superscript n] ; |
| -- |
Systems of particles ; |
| -- |
Angular momentum ; |
| -- |
Poisson brackets and Hamiltonian mechanics ; |
| -- |
The Kepler problem and the Runge-Lenz vector ; |
| Miscellaneous information |
Exercises -- |
| Title |
First approach to quantum mechanics: |
| -- |
Waves, particles, and probabilities ; |
| -- |
A few words about operators and their adjoints ; |
| -- |
Position and the position operator ; |
| -- |
Momentum and the momentum operator ; |
| -- |
The position and momentum operators ; |
| -- |
Axioms of quantum mechanics : operators and measurements ; |
| -- |
Time-evolution in quantum theory ; |
| -- |
The Heisenberg picture ; |
| -- |
Example : a particle in a box ; |
| -- |
Quantum mechanics for a particle in R [superscript n] ; |
| -- |
Systems of multiple particles ; |
| -- |
Physics notation ; |
| Miscellaneous information |
Exercises -- |
| Title |
The free Schrödinger equation: |
| -- |
Solution by means of the Fourier transform ; |
| -- |
Solution as a convolution ; |
| -- |
Propagation of the wave packet : first approach ; |
| -- |
Propagation of the wave packet : second approach ; |
| -- |
Spread of the wave packet ; |
| Miscellaneous information |
Exercises -- |
| Title |
Particle in a square well: |
| -- |
The time-independent Schrödinger equation ; |
| -- |
Domain questions and the matching conditions ; |
| -- |
Finding square-integrable solutions ; |
| -- |
Tunneling and the classically forbidden region ; |
| -- |
Discrete and continuous spectrum ; |
| Miscellaneous information |
Exercises -- |
| Title |
Perspectives on the spectral theorem: |
| -- |
The difficulties with the infinite-dimensional case ; |
| -- |
The goals of spectral theory ; |
| -- |
A guide to reading ; |
| -- |
The position operator ; |
| -- |
Multiplication operators ; |
| -- |
The momentum operator -- |
| -- |
The spectral theorem for bounded self-adjoint operators : statements: |
| -- |
Elementary properties of bounded operators ; |
| -- |
Spectral theorem for bounded self-adjoint operators, I ; |
| -- |
Spectral theorem for bounded self-adjoint operators, II ; |
| Miscellaneous information |
Exercises -- |
| Title |
The spectral theorem for bounded self-adjoint operators : proofs: |
| -- |
Proof of the spectral theorem, first version ; |
| -- |
Proof of the spectral theorem, second version ; |
| Miscellaneous information |
Exercises -- |
| Title |
Unbounded self-adjoint operators: |
| Miscellaneous information |
Introduction ; |
| Title |
Adjoint and closure of an unbounded operator ; |
| -- |
Elementary properties of adjoints and closed operators ; |
| -- |
The spectrum of an unbounded operator ; |
| -- |
Conditions for self-adjointness and essential self-adjointness ; |
| -- |
A counterexample ; |
| -- |
An example ; |
| -- |
The basic operators of quantum mechanics ; |
| -- |
Sums of self-adjoint operators ; |
| -- |
Another counterexample ; |
| Miscellaneous information |
Exercises -- |
| Title |
The spectral theorem for unbounded self-adjoint operators: |
| -- |
Statements of the spectral theorem ; |
| -- |
Stone's theorem and one-parameter unitary groups ; |
| -- |
The spectral theorem for bounded normal operators ; |
| -- |
Proof of the spectral theorem for unbounded self-adjoint operators ; |
| Miscellaneous information |
Exercises -- |
| Title |
The harmonic oscillator: |
| -- |
The role of the harmonic oscillator ; |
| -- |
The algebraic approach ; |
| -- |
The analytic approach ; |
| -- |
Domain conditions and completeness ; |
| Miscellaneous information |
Exercises -- |
| Title |
The uncertainty principle: |
| -- |
Uncertainty principle, first version ; |
| -- |
A counterexample ; |
| -- |
Uncertainty principle, second version ; |
| -- |
Minimum uncertainty states ; |
| Miscellaneous information |
Exercises -- |
| Title |
Quantization schemes for Euclidean space: |
| -- |
Ordering ambiguities ; |
| -- |
Some common quantization schemes ; |
| -- |
The Weyl quantization for R²[superscript n] ; |
| -- |
The "No go" theorem of Groenewold ; |
| Miscellaneous information |
Exercises -- |
| Title |
The Stone-Von Neumann theorem: |
| -- |
A heuristic argument ; |
| -- |
The exponentiated commutation relations ; |
| -- |
The theorem ; |
| -- |
The Segal-Bargmann space ; |
| Miscellaneous information |
Exercises -- |
| Title |
The WKB approximation: |
| Miscellaneous information |
Introduction ; |
| Title |
The old quantum theory and the Bohr-Sommerfeld condition ; |
| -- |
Classical and semiclassical approximations ; |
| -- |
The WKB approximation away from the turning points ; |
| -- |
The Airy function and the connection formulas ; |
| -- |
A rigorous error estimate ; |
| -- |
Other approaches ; |
| Miscellaneous information |
Exercises -- |
| Title |
Lie groups, Lie algebras, and representations: |
| Miscellaneous information |
Summary ; |
| Title |
Matrix Lie groups ; |
| -- |
Lie algebras ; |
| -- |
The matrix exponential ; |
| -- |
The Lie algebra of a matrix Lie group ; |
| -- |
Relationships between Lie groups and Lie algebras ; |
| -- |
Finite-dimensional representations of Lie groups and Lie algebras ; |
| -- |
New representations from old ; |
| -- |
Infinite-dimensional unitary representations ; |
| Miscellaneous information |
Exercises -- |
| Title |
Angular momentum and spin: |
| -- |
The role of angular momentum in quantum mechanics ; |
| -- |
The angular momentum operators in R³ ; |
| -- |
Angular momentum from the Lie algebra point of view ; |
| -- |
The irreducible representations of so(3) ; |
| -- |
The irreducible representations of SO(3) ; |
| -- |
Realizing the representations inside L²(S²) -- |
| -- |
Realizing the representations inside L²(M³) ; |
| -- |
Spin ; |
| -- |
Tensor products of representations : "addition of angular momentum" ; |
| -- |
Vectors and vector operators ; |
| Miscellaneous information |
Exercises -- |
| Title |
Radial potentials and the hydrogen atom: |
| -- |
Radial potentials ; |
| -- |
The hydrogen atom : preliminaries ; |
| -- |
The bound states of the hydrogen atom ; |
| -- |
The Runge-Lenz vector in the quantum Kepler problem ; |
| -- |
The role of spin ; |
| -- |
Runge-Lenz calculations ; |
| Miscellaneous information |
Exercises -- |
| Title |
Systems and subsystems, multiple particles: |
| Miscellaneous information |
Introduction ; |
| Title |
Trace-class and Hilbert-Schmidt operators ; |
| -- |
Density matrices : the general notion of the state of a quantum system ; |
| -- |
Modified axioms for quantum mechanics ; |
| -- |
Composite systems and the tensor product ; |
| -- |
Multiple particles : bosons and fermions ; |
| -- |
"Statistics" and the Pauli exclusion principle ; |
| Miscellaneous information |
Exercises -- |
| Title |
The path integral formulation of quantum mechanics: |
| -- |
Trotter product formula ; |
| -- |
Formal derivation of the Feynman path integral ; |
| -- |
The imaginary-time calculation ; |
| -- |
The Wiener measure ; |
| -- |
The Feynman-Kac formula ; |
| -- |
Path integrals in quantum field theory ; |
| Miscellaneous information |
Exercises -- |
| Title |
Hamiltonian mechanics on manifolds: |
| -- |
Calculus on manifolds ; |
| -- |
Mechanics on symplectic manifolds ; |
| Miscellaneous information |
Exercises -- |
| Title |
Geometric quantization on Euclidean space: |
| Miscellaneous information |
Introduction ; |
| Title |
Prequantization ; |
| -- |
Problems with prequantization ; |
| -- |
Quantization ; |
| -- |
Quantization of observables ; |
| Miscellaneous information |
Exercises -- |
| Title |
Geometric quantization on manifolds: |
| Miscellaneous information |
Introduction ; |
| Title |
Line bundles and connections ; |
| -- |
Prequantization ; |
| -- |
Polarizations ; |
| -- |
Quantization without half-forms ; |
| -- |
Quantization with half-forms : the real case ; |
| -- |
Quantization with half-forms : the complex case ; |
| -- |
Pairing maps ; |
| Miscellaneous information |
Exercises -- |
| Title |
A review of basic material: |
| -- |
Tensor products of vector spaces ; |
| -- |
Measure theory ; |
| -- |
Elementary functional analysis ; |
| -- |
Hilbert spaces and operators on them. |
| 526 ## - STUDY PROGRAM INFORMATION NOTE |
|---|
| Program name |
CSE |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Quantum theory |
| General subdivision |
Mathematics. |
| 9 (RLIN) |
39415 |
|
|---|
| Topical term or geographic name as entry element |
Quantum theory. |
|
|---|
| Topical term or geographic name as entry element |
Mathematical physics. |
|
|---|
| Topical term or geographic name as entry element |
Computer science. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Graduate texts in mathematics, |
| International Standard Serial Number |
0072-5285 ; |
| Volume number/sequential designation |
267. |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Item type |
Book |
