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QC174.12 .H35 2013
Local quantum physics
1996
Haag, Rudolf, 1922
SAL3 (offcampus storage) » QC174.12 .H32 1996
Quantum mechanics
1981
Hameka, Hendrik F.
SAL3 (offcampus storage) » QC174.12 .H35
Quantum theory for mathematicians
2013
Hall, Brian C.
Math & Statistics Library » QC174.12 .H35 2013
Quantum mechanics
2004
Hameka, Hendrik F.
»
The probable universe
1993
Han, M. Y.
SAL3 (offcampus storage) » QC174.12 .H358 1993
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Quantum theory for mathematicians / Brian C. Hall.
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Math & Statistics Library

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QC174.12 .H35 2013
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QC174.12 .H35 2013
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Author/Creator:
Hall, Brian C.,
author.
Language:
English.
Publication date:
2013
Copyright date:
2013
Copyright notice:
New York : Springer, [2013]
Publication:
©2013
Format:
Book
xvi, 554 pages ; 24 cm.
Bibliography:
Includes bibliographical references and index.
Contents:
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
Exercises
A first approach to classical mechanics
Motion in R1
Motion in Rn
Systems of particles
Angular momentum
Poisson brackets and hamiltonian mechanics
The kepler problem and the rungelenz vector
Exercises
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
Timeevolution in quantum theory
The heisenberg picture
Example : a particle in a box
Quantum mechanics for a particle in Rn
Systems of multiple particles
Physics notation
Exercises
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
Exercises
Particle in a Square Well
The timeindependent schrödinger equation
Domain questions and the matching conditions
Finding squareintegrable solutions
Tunneling and the classically forbidden region
Discrete and continuous spectrum
Exercises
Perspectives on the spectral theorem
The difficulties with the infinitedimensional case
The goals of spectral theory
A guide to reading
The position operator
Multiplication operators
The momentum operator
The spectral theorem for bounded selfadjoint operators : statements
Elementary properties of bounded operators
Spectral theorem for bounded selfadjoint operators, I
Spectral theorem for bounded selfadjoint operators, II
Exercises
The spectral theorem for bounded selfadjoint operators : proofs
Proof of the spectral theorem, first version
Proof of the spectral theorem, second version
Exercises
Unbounded selfadjoint operators
Introduction
Adjoint and closure of an unbounded operator
Elementary properties of adjoints and closed operators
The spectrum of an unbounded operator
Conditions for selfadjointness and essential selfadjointness
A counterexample
An example
The basic operators of quantum mechanics
Sums of selfadjoint operators
Another counterexample
Exercises
The spectral theorem for unbounded selfadjoint operators
Statements of the spectral theorem
Stone's theorem and oneparameter unitary groups
The spectral theorem for bounded normal operators
Proof of the spectral theorem for unbounded selfadjoint operators
Exercises
The harmonie oscillator
The role of the harmonie oscillator
The algebraic appfoach
The analytic approach
Domain conditions and completeness
Exercises
The uncertainty principle
Uncertainty principle, first version
A counterexample
Uncertainty principle, second version
Minimum uncertainty states
Exercises
Quantization schemes for euclidean space
Ordering ambiguities
Some common quantization schemes
The weyl quantization for R2n
The "No Go" theorem of groenewold
Exercises
The Stonevon Neumann Theorem
A Heuristic argument
The exponentiated commutation relations
The theorem
The segal bargmann space
Exercises
The WKB approximation
Introduction
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
Exercises
Lie groups, lie algebras, and representations
Summary
Matrix lie groups
Lie algebras
The matrix exponential
The lie algebra of a matrix lie group
Relationships between lie groups and lie algebras
Finitedimensional representations of lie groups and lie algebras
New representations from old
Infinitedimensional unitary representations
Exercises
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
Exercises
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
RungeLenz calculations
Exercises
Systems and subsystems, multiple particles
Introduction
Traceclass and hilbertschmidt 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
Exercises
The path integral formulation of quantum mechanics
Trotter product formula
Formal derivation of the feynman path integral
The imaginarytime calculation
The wiener measure
The feynmankac formula
Path integrals in quantum field theory
Exercises
Hamiltonian mechanics on manifolds
Calculus on manifolds
Mechanics on symplectic manifolds
Exercises
Geometrie quantization on euclidean space
Introduction
Prequantization
Problems with prequantization
Quantization
Quantization of observables
Exercises
Geometrie quantization on manifolds
Introduction
Line bundles and connections
Prequantization
Polarizations
Quantization without halfforms
Quantization with halfforms : the real case
Quantization with halfforms : the complex case
Pairing maps
Exercises
A review of basic material
Tensor products of vector spaces
Measure theory
Elementary functional analysis
Hilbert spaces and operators on them
References
Index.
Series:
Graduate texts in mathematics, 00725285 ; 267
Graduate texts in mathematics ;
267.
Subjects:
Quantum theory
>
Mathematics.
ISBN:
9781461471158
146147115X
Catkey: 10196598
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