Calculus for Functions of Noncommuting Operators and General Phase-Space Methods in Quantum Mechanics. I. Mapping Theorems and Ordering of Functions of Noncommuting Operators

1970 ◽  
Vol 2 (10) ◽  
pp. 2161-2186 ◽  
Author(s):  
G. S. Agarwal ◽  
E. Wolf
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Noncommuting Operators ◽  
General Phase ◽  
Phase Space Methods

scholarly journals Modes and Noise Propagation in Phase Space

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
J. S. Ben-Benjamin ◽  
L. Cohen
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Dispersion Relation ◽  
Wigner Distribution ◽  
Hermitian Operator ◽  
Type Equation ◽  
Hamiltonian Operator ◽  
Dispersive Media ◽  
Phase Space Methods ◽  
Complex Dispersion

AbstractWe show that phase space methods developed for quantum mechanics, such as the Wigner distribution, can be effectively used to study the evolution of nonstationary noise in dispersive media. We formulate the issue in terms of modes and show how modes evolve and how they are effected by sources.We show that each mode satisfies a Schrödinger type equation where the “Hamiltonian” may not be Hermitian. The Hamiltonian operator corresponds to dispersion relationwhere thewavenumber is replaced by the wavenumber operator. A complex dispersion relation corresponds to a non Hermitian operator and indicates that we have attenuation. A number of examples are given.

BOUND STATES FOR SCHRÖDINGER HAMILTONIANS: PHASE SPACE METHODS AND APPLICATIONS

1996 ◽  
Vol 08 (04) ◽  
pp. 503-547 ◽  
Author(s):  
PH. BLANCHARD ◽  
J. STUBBE
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Dynamical Systems ◽  
Bound States ◽  
Energy Levels ◽  
Schrödinger Operators ◽  
Particle Systems ◽  
Existence And Nonexistence ◽  
Phase Space Methods ◽  
Special Case

Properties of bound states for Schrödinger operators are reviewed. These include: bounds on the number of bound states and on the moments of the energy levels, existence and nonexistence of bound states, phase space bounds and semi-classical results, the special case of central potentials, and applications of these bounds in quantum mechanics of many particle systems and dynamical systems. For the phase space bounds relevant to these applications we improve the explicit constants.

scholarly journals Nonequilibrium dynamics of spin-boson models from phase-space methods

2017 ◽  
Vol 96 (3) ◽  
Author(s):  
Asier Piñeiro Orioli ◽  
Arghavan Safavi-Naini ◽  
Michael L. Wall ◽  
Ana Maria Rey
Keyword(s):  
Phase Space ◽  
Nonequilibrium Dynamics ◽  
Phase Space Methods
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