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Oxford University Press eBooks

Extracting information from the wavefunction

Peter Joshua Atkins, Julio de Paula, Ronald Friedman

Published Dec 12, 2013• 0 citations
Publisher

Abstract

Contents Postulate III: quantum mechanical operators 47 Brief illustration 6.1: The kinetic energy operator in two dimensions 49 Postulate IV: eigenvalues and eigenfunctions 50 Example 6.1: Identifying an eigenfunction 50 Brief illustration 6.2: The wavefunction as an eigenfunction 51 Checklist of concepts 52...
DOI
10.1093/hesc/9780199609819.003.0009

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Oxford University Press eBooks•Dec 12, 2013•0 citations
Part 1: the need for the quantum mechanics quantization of radiation the special theory of relativity wave-particle duality the nature of matter waves the uncertainty principle the Bohr atom. Part 2 Schrodinger's equation: the postulates of quantum mechanics the wave equation the wave equation in three dimensions the time-independent Schrodinger equation stationary states normalisation probability flux physical constraints on the wave-function wave packets Gaussian wave-packets and the uncertainty principle. Part 3 One-dimensional potential wells: potential wells the one-dimensional infinite square well discussion of infinite square-well results eigenvalue equations the finite square well finite square well eigenfunctions the control of the wave-function by the wave equation numerical integration of Schrodinger's equation continuum solutions of the square-well potential interpretation of unbound-particle wave functions the double potential well the quantum bouncer electric fields and the tilted well the harmonic oscillator - introduction the quantum oscillator discussion of harmonic oscillator eigenvalues and eigenfunctions the classical probability density more potential wells. Part 4 Schrodinger's equation in three dimensions: particle in a three dimensional box degeneracy Schrodingers equation in spherical polar coordinates - the hydrogen atom normalisation. Part 5 Formal development of quantum mechanics: eigenvalues equations, operators and measurements the momentum operator, eigenvalues and eigenfunctions the position operator and its eigenfunctions Hermitian operators orthogonality of eigenfunctions the expansion postulate example - the b-decay of tritium expectation values compatibility of observables - commutators non-commuting operators time-dependence of expectation values - Ehrenfest's theorem abstract operators - the parity operator, matrix mechanics. Part 6 Angular momentum: angular momentum operators angular momentum commutators angular momentum eigenvalues and eigenfunctions interpretation of angular momentum eigenvalues interpretation of angular momentum eigenfunctions the Stern-Gerlach apparatus and electron spin spin operators - the Pauli Spin matrices the Zeeman effect measurements in quantum mechanics. Part 7 Spherically symmetric potential wells: the rigid rotator the radial equation the hydrogen atom and hydrogen like ions the isotropic harmonic oscillator molecular vibrations - the Morse potential the spherical square well general properties of spherically symmetric potential wells. (Part contents)
(NOTE: All chapters conclude with Final Thoughts, and Exercises and Problems most also include Annotated Selected Readings.)I. WHAT'S IT ALL ABOUT?: A QUALITATIVE INTRODUCTION. 1. Introductory: Why Quantum Physics? 2. Into the Microworld: Duality and the Double Slit. II. STARTING FROM SCRATCH. 3. First Postulates: The State Function and Its Interpretation. 4. An Illustrative Interlude: Wave Packets in One Dimension. 5. Observables in Quantum Physics: A Pragmatist's Approach. 6. A Quantum Equation of Motion: The Schroedinger Equation At Last. 7. Simplifying Matters: The Time-Independent Schroedinger Equation. III. EXAMPLES, EXAMPLES, EXAMPLES. 8. States of a Particle in One Dimension I: Mainly Piecewise-Constant Potentials. 9. States of a Particle in One Dimension II: Mainly Continuous Potentials. IV. TOOLS OF THE TRADE MORE FORMALISM. 10. Operators in Quantum Mechanics I: The Importance of Being Hermitian. 11. Operators in Quantum Mechanics II: To Commute or Not to Commute. 12. Eigenfunction Expansions: How to Solve Any Problem in Quantum Mechanics. 13. Altered States: The Great Measurement Mystery. Appendixes. A. SI Units (The International System of Units. B. Fundamental Constants in SI (and CGS) Units. C. Order-of-Magnitude Estimates. D. Conversion Tables. E. Prefix Dictionary. F. A User's Guide to Atomic Units. G. The Greek Alphabet. H. Handy Trigonometric identities. I. Integrals You Should Know. J. Integrals Involving the Gaussian Function. K. Review of Complex Numbers. L. The Dirac Delta Function. Bibliography. Index.