An analysis of the states in the phase space: the energy levels of quantum systems

1996 ◽  
Vol 111 (2) ◽  
pp. 193-215 ◽  
Author(s):  
S. Tosto
Keyword(s):  
Phase Space ◽  
Energy Levels ◽  
Quantum Systems

Invariance Groups in Classical and Quantum Mechanics

1973 ◽  
Vol 28 (3-4) ◽  
pp. 538-540 ◽  
Author(s):  
D. J. Simms
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Energy Levels ◽  
Classical Mechanics ◽  
Symmetry Groups ◽  
Casimir Invariants ◽  
Classical Phase Space ◽  
Invariance Groups ◽  
Classical And Quantum Mechanics

AbstractThis is a report on some new relations and analogies between classical mechanics and quantum mechanics which arise out of the work of Kostant and Souriau. Topics treated are i) the role of symmetry groups; ii) the notion of elementary system and the role of Casimir invariants; iii) energy levels; iv) quantisation in terms of geometric data on the classical phase space. Some applications are described.

Approximate energy levels of central field bound quantum systems

1983 ◽  
Vol 51 (12) ◽  
pp. 1150-1151 ◽  
Author(s):  
Francisco M. Fernández ◽  
Eduardo A. Castro
Keyword(s):  
Energy Levels ◽  
Quantum Systems ◽  
Central Field

scholarly journals Phase space formulation of density operator for non-Hermitian Hamiltonians and its application in quantum theory of decay

2018 ◽  
Vol 32 (25) ◽  
pp. 1850276 ◽  
Author(s):  
Ludmila Praxmeyer ◽  
Konstantin G. Zloshchastiev
Keyword(s):  
Phase Space ◽  
Density Operator ◽  
Quantum Systems ◽  
Matrix Approach ◽  
Weyl Transform ◽  
Energy Eigenvalues ◽  
Decay Constants ◽  
Dissipative Effects ◽  
Mean Lifetime ◽  
Space Formulation

The Wigner–Weyl transform and phase space formulation of a density matrix approach are applied to a non-Hermitian model which is quadratic in positions and momenta. We show that in the presence of a quantum environment or reservoir, mean lifetime and decay constants of quantum systems do not necessarily take arbitrary values, but could become functions of energy eigenvalues and have a discrete spectrum. It is demonstrated also that a constraint upon mean lifetime and energy appears, which is used to derive the resonance conditions at which long-lived states occur. The latter indicate that quantum dissipative effects do not always lead to decay but, under certain conditions, can support stability of a system.

Integrability and nonintegrability of quantum systems. II. Dynamics in quantum phase space

1990 ◽  
Vol 42 (12) ◽  
pp. 7125-7150 ◽  
Author(s):  
Wei-Min Zhang ◽  
Da Hsuan Feng ◽  
Jian-Min Yuan
Keyword(s):  
Phase Space ◽  
Quantum Systems ◽  
Quantum Phase

Approximate energy levels and sizes of bound quantum systems

1982 ◽  
Vol 50 (1) ◽  
pp. 53-59 ◽  
Author(s):  
H. A. Gersch ◽  
C. H. Braden
Keyword(s):  
Energy Levels ◽  
Quantum Systems

Finite element distributions in statistical theory of energy levels in quantum systems

1999 ◽  
Vol 125 (3-4) ◽  
pp. 260-274 ◽  
Author(s):  
Maciej M. Duras ◽  
Krzysztof Sokalski
Keyword(s):  
Finite Element ◽  
Statistical Theory ◽  
Energy Levels ◽  
Quantum Systems

scholarly journals Phase space theory for open quantum systems with local and collective dissipative processes

2020 ◽  
Vol 54 (3) ◽  
pp. 035303
Author(s):  
Konrad Merkel ◽  
Valentin Link ◽  
Kimmo Luoma ◽  
Walter T Strunz
Keyword(s):  
Phase Space ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Space Theory ◽  
Open Quantum ◽  
Dissipative Processes ◽  
Phase Space Theory

Simplified P-representation operator correspondence applied to quantum systems with generalized Kerr nonlinearity

2019 ◽  
Vol 33 (28) ◽  
pp. 1950340 ◽  
Author(s):  
S. Chiangga ◽  
S. Pitakwongsaporn ◽  
Till D. Frank
Keyword(s):  
Energy Levels ◽  
Kerr Nonlinearity ◽  
Quantum Systems ◽  
Matter Wave ◽  
Quantum Oscillator ◽  
Text Representation ◽  
Nonlinear Quantum ◽  
Quantum Optical ◽  
Field Oscillation ◽  
Quadratic And Cubic Nonlinearities

A simplified operator correspondence scheme is derived to address nonlinear quantum systems within the framework of the [Formula: see text]-representation. The simplified method is applied to a general nonlinear quantum oscillator model that has been used in the literature to describe nonlinear quantum optical and matter wave systems. The [Formula: see text]-representation evolution equation for the model is derived for arbitrary nonlinearity exponents. It is shown that in the high temperature case, the [Formula: see text]-representation is sufficient to describe the model and its associated systems such that there is no need to use alternative, mathematically more involved representations. Systems with quadratic and cubic nonlinearities are considered in more detail. Distributions for the energy levels and photon and particle numbers are obtained within the framework of the [Formula: see text]-representation. Moreover, the electrical field oscillation frequency dependency is studied numerically when interpreting the model as model for quantum optical nonlinear oscillators.

scholarly journals ON THE STABILITY OF PERIODICALLY TIME-DEPENDENT QUANTUM SYSTEMS

2008 ◽  
Vol 20 (06) ◽  
pp. 725-764 ◽  
Author(s):  
P. DUCLOS ◽  
E. SOCCORSI ◽  
P. ŠŤOVÍČEK ◽  
M. VITTOT
Keyword(s):  
Transition Probabilities ◽  
Initial Conditions ◽  
Energy Levels ◽  
Sufficient Conditions ◽  
Energy Operator ◽  
Mean Value ◽  
Quantum Systems ◽  
Time Dependent ◽  
Dense Subspace ◽  
Periodically Driven

The main motivation of this article is to derive sufficient conditions for dynamical stability of periodically driven quantum systems described by a Hamiltonian H(t), i.e. conditions under which it holds true sup t ∈ ℝ|〈ψt, H(t)ψt〉| < ∞ where ψt denotes a trajectory at time t of the quantum system under consideration. We start from an analysis of the domain of the quasi-energy operator. Next, we show, under certain assumptions, that if the spectrum of the monodromy (Floquet) operator U(T, 0) is pure point then there exists a dense subspace of initial conditions for which the mean value of the energy is uniformly bounded in the course of time. Further, we show that if the propagator admits a differentiable Floquet decomposition then ‖H(t)ψt‖ is bounded in time for any initial condition ψ0, and one employs the quantum KAM algorithm to prove the existence of this type of decomposition for a fairly large class of H(t). In addition, we derive bounds uniform in time on transition probabilities between different energy levels, and we also propose an extension of this approach to the case of a higher order of differentiability of the Floquet decomposition. The procedure is demonstrated on a solvable example of the periodically time-dependent harmonic oscillator.

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