UID:
almahu_9948342718702882
Umfang:
1 online resource (various pagings) :
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illustrations.
ISBN:
9780750321792
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9780750321808
Serie:
IOP ebooks. [2020 collection]
Inhalt:
This book, the first of a two-volume set, provides a comprehensive introduction to quantum mechanics for advanced undergraduate and postgraduate students entering the field of nuclear structure studies via two-state systems: both polarized photons and spin-1/2 particles. This leads to the logic behind the physical structure and an axiomatic formulation using linear spaces and operators. The one-dimensional harmonic oscillator is used to illustrate the mechanics of quantized systems, reaching to time dependence and coherent states. Measurement theory is introduced. The transformation theory of space and time leads to wave functions. The role of group theory and rotations then leads to the quantization of angular momentum. Central force problems are handled algebraically. The development is completed with quantization of motion of a charged particle in a magnetic field. Part of IOP Series in Nuclear Spectroscopy and Nuclear Structure.
Anmerkung:
"Version: 20191201"--Title page verso.
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1. A theory of polarized photons -- 1.1. Polarized lightwaves -- 1.2. Polarized photons -- 1.3. Uncertainty in experiments -- 1.4. Dirac bracket notation -- 1.5. Transformation properties of polarizing filter measurements -- 1.6. Multiples of kets -- 1.7. Exercises
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2. A theory of the Stern-Gerlach experiment for spin-1-2 particles -- 2.1. The Stern-Gerlach experiment -- 2.2. Sequences of Stern-Gerlach measurements -- 2.3. State representation for spin-1-2 particles -- 2.4. The choice of basis kets -- 2.5. Exercises -- 2.6. An introduction to operators for spin-1-2 particles -- 2.7. Exercises
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3. The axioms of quantum mechanics -- 3.1. Global axioms of observation -- 3.2. Axioms for quantum mechanical observations -- 3.3. Axioms for the mathematical structure of quantum mechanics -- 3.4. Axioms for the incorporation of h in quantum mechanics -- 3.5. Exercise
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4. Linear spaces and linear operators -- 4.1. Definitions and theorems for linear spaces and linear operators -- 4.2. Linear spaces, Dirac bras and kets, and operators -- 4.3. Outer products of Dirac bras and kets -- 4.4. Exercises
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5. The harmonic oscillator -- 5.1. The quantum mechanical one-dimensional harmonic oscillator -- 5.2. The quantum mechanical two-dimensional harmonic oscillator -- 5.3. Time dependence of the one-dimensional quantum harmonic oscillator -- 5.4. Exercises -- 5.5. Coherent states and the one-dimensional harmonic oscillator
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6. Representations : matrices -- 6.1. Basics of matrix manipulation -- 6.2. Exercises -- 6.3. The two-level mixing problem -- 6.4. Exercises -- 6.5. Unitary transformations and matrix diagonalization -- 6.6. Exercises -- 6.7. Matrix diagonalization : the Jacobi method -- 6.8. Exercise
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7. Observables and measurements -- 7.1. Basic concepts -- 7.2. The uncertainty relation -- 7.3. Exercises -- 7.4. Mixtures and the density matrix
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8. Representations : position, momentum, wave functions, and function spaces -- 8.1. The concept of a wave function -- 8.2. The quantum mechanical structure of position and momentum -- 8.3. The wave-like properties of matter -- 8.4. Exercises
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9. Quantum dynamics : time evolution and the Schrödinger and Heisenberg pictures -- 9.1. Basic relations -- 9.2. Spin precession -- 9.3. Exercises -- 9.4. Correlation amplitude and the energy-time uncertainty relation -- 9.5. The Schrödinger and Heisenberg pictures -- 9.6. The free particle in the Heisenberg picture -- 9.7. Schrödinger's wave equation -- 9.8. Exercises -- 9.9. Alternative derivation of the energy-time uncertainty relation -- 9.10. Time-dependent phenomena -- 9.11. Time-dependent two-state problems -- 9.12. Exercise
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10. Rotations and continuous transformation groups -- 10.1. Elements of group theory -- 10.2. Matrix groups -- 10.3. Exercises -- 10.4. Rotations in physical space -- 10.5. Exercise -- 10.6. Rotations of quantum mechanical states -- 10.7. Exercise
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11. Angular momentum and spin in quantum mechanics -- 11.1. The algebra of angular momentum in quantum mechanics -- 11.2. Algebraic solution of the quantum mechanical angular momentum problem -- 11.3. Exercises
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12. Central force problems -- 12.1. General features of central force problems -- 12.2. Central force problems, factorization algebra and isospectral Hamiltonians -- 12.3. The hydrogen atom central force problem -- 12.4. The three-dimensional isotropic harmonic oscillator central force problem -- 12.5. The three-dimensional isotropic infinite square well central force problem -- 12.6. Exercises -- 12.7. Central force problems and so(2, 1) or su(1, 1) algebra -- 12.8. so(2, 1) solution for the hydrogen atom -- 12.9. so(2, 1) solution for the three-dimensional isotropic harmonic oscillator
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13. Motion of an electron in a uniform magnetic field -- 13.1. Maxwell's equations -- 13.2. The Landau level problem -- 13.3. Time dependence of the Landau problem -- 13.4. Exercises
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Appendices. A. Commutator bracket relations for central force problems -- B. Radial wave functions for the hydrogen atom and the three-dimensional isotropic harmonic oscillator.
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Also available in print.
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Mode of access: World Wide Web.
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System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.
Weitere Ausg.:
Print version: ISBN 9780750321778
Weitere Ausg.:
ISBN 9780750321785
Sprache:
Englisch
DOI:
10.1088/978-0-7503-2179-2
URL:
https://iopscience.iop.org/book/978-0-7503-2179-2
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