Title:
Principles of quantum mechanics / R. Shankar.
Main Entry:
Shankar, Ramamurti, author.
Publisher:
Plenum Press,
Publication Date:
�1994.
Publication Place:
New York :
ISBN:
0306447908
9780306447907
Subject:
Quantum theory.
Quantum theory.
Quantenmechanik
Kwantummechanica.
Th�eorie quantique -- Manuels d'enseignement.
Th�eorie quantique.
Quantum theory
Edition:
2nd ed.
Contents:
Mathematical Introduction. Linear Vector Spaces: Basics. Inner Product Spaces. Dual Spaces and the Dirac Notation. Subspaces. Linear Operators. Matrix Elements of Linear Operators. Active and Passive Transformations. The Eigenvalue Problem. Functions of Operators and Related Concepts. Generalization to Infinite Dimensions -- Review of Classical Mechanics.
The Principle of Least Action and Lagrangian Mechanics. The Electromagnetic Lagrangian. The Two-Body Problem. How Smart Is a Particle? The Hamiltonian Formalism. The Electromagnetic Force in the Hamiltonian Scheme. Cyclic Coordinates, Poisson Brackets, and Canonical Transformations. Symmetries and Their Consequences -- All Is Not Well with Classical Mechanics. Particles and Waves in Classical Physics.
An Experiment with Waves and Particles (Classical). The Double-Slit Experiment with Light. Matter Waves (de Broglie Waves) -- The Postulates -- a General Discussion. The Postulates. Discussion of Postulates I-III. The Schrodinger Equation (Dotting Your i's and Crossing your h's) -- Simple Problems in One Dimension. The Free Particle. The Particle in a Box. The Continuity Equation for Probability.
The Single-Step Potential: a Problem in Scattering. The Double-Slit Experiment. Some Theorems -- The Classical Limit -- The Harmonic Oscillator. Why Study the Harmonic Oscillator? Review of the Classical Oscillator. Quantization of the Oscillator (Coordinate Basis). The Oscillator in the Energy Basis. Passage from the Energy Basis to the X Basis -- The Path Integral Formulation of Quantum Theory.
The Path Integral Recipe. Analysis of the Recipe. An Approximation to U(t) for the Free Particle. Path Integral Evaluation of the Free-Particle Propagator. Equivalence to the Schrodinger Equation. Potentials of the Form V = a + bx + cx[superscript 2] + dx + exx -- The Heisenberg Uncertainty Relations. Derivation of the Uncertainty Relations. The Minimum Uncertainty Packet. Applications of the Uncertainty Principle.
Multielectron Atoms and the Periodic Table -- Spin. What is the Nature of Spin? Kinematics of Spin. Spin Dynamics. Return of Orbital Degrees of Freedom -- Addition of Angular Momenta. A Simple Example. The General Problem. Irreducible Tensor Operators. Explanation of Some "Accidental" Degeneracies -- Variational and WKB Methods. The Variational Method.
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