Related papers: A position-dependent mass harmonic oscillator and …
In this paper, we examine the thermodynamic behavior of a quantum harmonic oscillator with a position-dependent mass (PDM), where spatial inhomogeneity is modeled through a deformation parameter {\alpha}. Based on the exact energy spectrum,…
This paper is devoted to find the exact solution of the harmonic oscillator in a position-dependent 4-dimensional noncommutative phase space. The noncommutative phase space that we consider is described by the commutation relations between…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
Relation between Bopp-Kubo formulation and Weyl-Wigner-Moyal symbol calculus, and non-commutative geometry interpretation of the phase space representation of quantum mechanics are studied. Harmonic oscillator in phase space via creation…
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master…
Quantum canonical transformations corresponding to time-dependent diffeomorphisms of the configuration space are studied. A special class of these transformations which correspond to time-dependent dilatations is used to identify a…
The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrodinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb,…
A new deformed canonical commutation relation, generalizing various known deformations, is defined together with its structure function of deformation. Then, the related irreducible representations are characterized and classified. Finally,…
We consider classical theories described by Hamiltonians $H(p,q)$ that have a non-degenerate minimum at the point where generalized momenta $p$ and generalized coordinates $q$ vanish. We assume that the sum of squares of generalized momenta…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
The classical and quantum mechanical correspondence for constant mass settings is used, along with some point canonical transformation, to find the position-dependent mass (PDM) classical and quantum Hamiltonians. The comparison between the…
We study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics. We extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time…
A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases…
Canonical transformations using the idea of quantum generating functions are applied to construct a quantum Hamilton-Jacobi theory, based on the analogy with the classical case. An operator and a c-number forms of the time-dependent quantum…
Different routes towards the canonical formulation of a classical theory result in different canonically equivalent Hamiltonians, while their quantum counterparts are related through appropriate unitary transformation. However, for…
The Bohr Hamiltonian describing the collective motion of atomic nuclei is modified by allowing the mass to depend on the nuclear deformation. Exact analytical expressions are derived for spectra and wave functions in the case of a…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and…
An essential prerequisite for the study of q-deformed physics are particle states in position and momentum representation. In order to relate x- and p-space by Fourier transformations the appropriate q-exponential series related to…