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Time-Dependent Harmonic Oscillator and the Wigner Function

Seoktae Koh

New Physics Sae MulliDec 30, 20190 citations

Time-dependent invariants for dirac equation and Newton–Wigner position operator

Vladimir I. Man’ko, R. Vilela Mendes

For Dirac equation, operator-invariants containing explicit time-dependence in parallel to known time-dependent invariants of nonrelativistic Schrödinger equation are introduced and discussed. As an example, a free Dirac particle is considered and new invariants are constructed for it. The integral of motion, which is initial Newton-Wigner position operator, is obtained explicitly for a free Dirac particle. For such particle with kick modeled by delta-function of time, the time-depending integral, which has physical meaning of initial momentum, is found.For Dirac equation, operator-invariants containing explicit time-dependence in parallel to known time-dependent invariants of nonrelativistic Schrödinger equation are introduced and discussed. As an example, a free Dirac particle is considered and new invariants are constructed for it. The integral of motion, which is initial Newton-Wigner position operator, is obtained explicitly for a free Dirac particle. For such particle with kick modeled by delta-function of time, the time-depending integral, which has physical meaning of initial momentum, is found.

arXiv:quant-ph/9702035Physica ScriptaNov 1, 19975 citations

Wigner functions in the Paul trap

G. Schrade, Vladimir I. Man’ko, Wolfgang P. Schleich +1 more

The authors review the theory of the harmonic oscillator with time-dependent frequency by means of an approach based on an operator constant of the motion. With the help of this operator constant we define the ground state, the excited states and a coherent state of the oscillator and discuss the time dependence of these states through their Wigner functions. The authors derive the Wigner function of an arbitrary state at time t evolving in the time-dependent harmonic potential. Moreover, they calculate the correlation coefficient between position and momentum, which appears in the Schrodinger uncertainty relation. The authors illustrate their results for the example of a charged particle in the Paul trap.The authors review the theory of the harmonic oscillator with time-dependent frequency by means of an approach based on an operator constant of the motion. With the help of this operator constant we define the ground state, the excited states and a coherent state of the oscillator and discuss the time dependence of these states through their Wigner functions. The authors derive the Wigner function of an arbitrary state at time t evolving in the time-dependent harmonic potential. Moreover, they calculate the correlation coefficient between position and momentum, which appears in the Schrodinger uncertainty relation. The authors illustrate their results for the example of a charged particle in the Paul trap.

Quantum and Semiclassical Optics Journal of the European Optical Society Part BJun 1, 199573 citations

Dynamical Equations for the Wigner Functions

Jens Peder Dahl

Springer eBooksJan 1, 198320 citations

Wigner Function of a Time-dependent Inverted Harmonic Oscillator

Seoktae Koh

New Physics Sae MulliJan 31, 20232 citations

TIME-DEPENDENT INVARIANTS FOR DIRAC EQUATION AND NEWTON–WIGNER POSITION OPERATOR

For Dirac equation, operator-invariants containing explicit time-dependence in parallel to known time-dependent invariants of nonrelativistic Schrödinger equation are introduced and discussed. As an example, a free Dirac particle is considered and new invariants are constructed for it. The integral of motion, which is initial Newton–Wigner position operator, is obtained explicitly for a free Dirac particle. For such particle with kick modeled by delta-function of time, the time-depending integral, which has physical meaning of initial momentum, is found. 1For Dirac equation, operator-invariants containing explicit time-dependence in parallel to known time-dependent invariants of nonrelativistic Schrödinger equation are introduced and discussed. As an example, a free Dirac particle is considered and new invariants are constructed for it. The integral of motion, which is initial Newton–Wigner position operator, is obtained explicitly for a free Dirac particle. For such particle with kick modeled by delta-function of time, the time-depending integral, which has physical meaning of initial momentum, is found. 1

Jan 1, 19970 citations

A New Approach for Calculation of Time-Dependent Wigner Operator

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