Related papers: Quantum derivation of Manley Rowe type relations
The quantum kinetic equation used in the study of weak turbulence is reconsidered in the context of a theory with a generic quartic interaction. The expectation value of the time derivative of the mode number operators is computed in a…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
Equivalent relations between quantum mechanical systems in the Robertson-Walker (RW) background metric and quantum dynamics with an induced quadratic background potential are derived in this work. Two elementary applications, which include…
For the models of $N$-body identical harmonic oscillators interacting through potentials of homogeneous degree -2, the unitary operator that transforms a system of time-dependent parameters into that of unit spring constant and unit mass of…
We apply the Lewis-Riesenfeld invariant method for the harmonic oscillator with time dependent mass and frequency to the modes of a charged scalar field that propagates in a curved, homogeneous and isotropic spacetime. We recover the…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…
The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
We revise the Lewis-Riesenfeld invariant method for solving the quantum time-dependent harmonic oscillator in light of the Quantum Arnold Transformation previously introduced and its recent generalization to the Quantum…
This study explores the time-dependent Dunkl-Pauli oscillator in two dimensions. We constructed the Dunkl-Pauli Hamiltonian, which incorporates a time-varying magnetic field and a harmonic oscillator characterized by time-dependent mass and…
We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators $H(t)$ that generate a real phase in their time-evolution. This involves the use of invariant operators $I_{PH}(t)$ that are pseudo-Hermitian with…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
Lorentz-covariant harmonic oscillator wave functions are constructed from the Lorentz-invariant oscillator differential equation of Feynman, Kislinger, and Ravndal for a two-body bound state. The wave functions are not invariant but…
We consider the problem of the driven harmonic oscillator in the probability representation of quantum mechanics, where the oscillator states are described by fair nonnegative probability distributions of position measured in rotated and…
The generation of continuous-variable multipartite entangled states is important for several protocols of quantum information processing and communication, such as one-way quantum computation or controlled dense coding. In this article we…
In the first days of quantum mechanics Dirac pointed out an analogy between the time-dependent coefficients of an expansion of the Schr\"odinger equation and the classical position and momentum variables solving Hamilton's equations. Here…
We construct the integrals of motion for several models of the quantum damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic…
Covariant phase space quantization attempts to quantize the full space of classical solutions, leading to a quantum theory in which the usual time coordinate is missing. In this paper we explore how the time evolution of the quantum states…