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Lectures on Quantum Mechanics for Mathematics Students

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ISBN-10: 082184699X

ISBN-13: 9780821846995

Edition: 2009

Authors: L. D. Faddeev, O. A. Yakubovskii

List price: $44.00
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This volume is based on notes from the course developed and taught for more than 30 years at the Department of Mathematics at Leningrad University. The goal of the course was to present quantum mechanics and its mathematical context to students in mathematics.
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Book details

List price: $44.00
Copyright year: 2009
Publisher: American Mathematical Society
Publication date: 3/30/2009
Binding: Paperback
Pages: 234
Size: 5.50" wide x 8.25" long x 0.50" tall
Weight: 0.682
Language: English

The algebra of observables in classical mechanics
States Liouville's theorem, and two pictures of motion in classical mechanics
Physical bases of quantum mechanics
A finite-dimensional model of quantum mechanics
States in quantum mechanics
Heisenberg uncertainty relations
Physical meaning of the eigenvalues and eigenvectors of observables
Two pictures of motion in quantum mechanics.
The Schrodinger equation.
Stationary states Quantum mechanics of real systems.
The Heisenberg commutation relations
Coordinate and momentum representations
"Eigenfunctions" of the operators $Q$ and $P$
The energy, the angular momentum, and other examples of observables
The interconnection between quantum and classical mechanics.
Passage to the limit from quantum mechanics to classical mechanics
One-dimensional problems of quantum mechanics.
A free one-dimensional particle
The harmonic oscillator
The problem of the oscillator in the coordinate representation
Representation of the states of a one-dimensional particle in the sequence space $l_2$
Representation of the states for a one-dimensional particle in the space $\mathcal{D}$ of entire analytic functions
The general case of one-dimensional motion
Three-dimensional problems in quantum mechanics.
A three-dimensional free particle
A three-dimensional particle in a potential field
Angular momentum
The rotation group
Representations of the rotation group
Spherically symmetric operators
Representation of rotations by $2\times2$ unitary matrices
Representation of the rotation group on a space of entire analytic functions of two complex variables
Uniqueness of the representations $D_j$
Representations of the rotation group on the space $L^2(S^2)$.
Spherical functions
The radial Schrodinger equation
The hydrogen atom.
The alkali metal atoms Perturbation theory The variational principle Scattering theory.
Physical formulation of the problem
Scattering of a one-dimensional particle by a potential barrier
Physical meaning of the solutions $\psi_1$ and $\psi_2$
Scattering by a rectangular barrier
Scattering by a potential center
Motion of wave packets in a central force field
The integral equation of scattering theory
Derivation of a formula for the cross-section
Abstract scattering theory
Properties of commuting operators
Representation of the state space with respect to a complete set of observables
Spin Spin of a system of two electrons
Systems of many particles.
The identity principle Symmetry of the coordinate wave functions of a system of two electrons.
The helium atom Multi-electron atoms.
One-electron approximation The self-consistent field equations
Mendeleev's periodic system of the elements
Lagrangian formulation of classical mechanics