Related papers: Remarks on the harmonic oscillator with a minimal …
We show that and how the Coulomb potential can be regularized and solved exactly at the imaginary couplings. The new spectrum of energies is real and bounded as expected, but its explicit form proves totally different from the usual…
In Phys. Rev. A 70, 032104 (2004), M. Montesinos and G. F. Torres del Castillo consider various symplectic structures on the classical phase space of the two-dimensional isotropic harmonic oscillator. Using Dirac's quantization condition,…
Using heuristic arguments alone, based on the properties of the wavefunctions, we obtain the energy eigenvalues and the corresponding eigenfunctions of the one-dimensional harmonic oscillator. This approach is considerably simpler and is…
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,…
We consider two-dimensional harmonic oscillator in the complex Bargmann-Fock-Segal representation with $T^*{\mathbb R}^{2}={\mathbb C}^2$ as classical phase space. We show that the eigenfunctions $\psi_n$ of the quantum Hamiltonian…
The quantum harmonic oscillator with parity-time ($\mathcal{PT}$) symmetry, obtained from the ordinary (Hermitian) quantum harmonic oscillator by an imaginary displacement of the spatial coordinate, provides an important and…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
We establish the existence of homoclinic solutions for suitable systems of nonlocal equations whose forcing term is of gradient type. The elliptic operator under consideration is the fractional Laplacian and the potentials that we take into…
A mapping is obtained relating radial screened Coulomb systems with low screening parameters to radial anharmonic oscillators in N-dimensional space. Using the formalism of supersymmetric quantum mechanics, it is shown that exact solutions…
It is shown that the rate of corrections to the hydrogen atom and harmonic oscillator due to profound quantum-gravitational effect of space-time dimension running/reduction coincides well with those obtained by means of the minimum-length…
It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper we generalize this property to finite-dimensional commutative algebras. We prove that if some basis of a…
Based on the nonperturbative analysis, we show that the classical motion of harmonic oscillator derived from the deformed QM is manifestly in contradiction with observations. For this reason, we take an alternate way for estimating the…
We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be…
We study the Schr\"odinger operator with a potential given by the sum of the potentials for harmonic oscillator and imaginary cubic oscillator and we focus on its pseudospectral properties. A summary of known results about the operator and…
Classical oscillator differential equation is replaced by the corresponding (finite time) difference equation. The equation is, then, symmetrized so that it remains invariant under the change d going to -d, where d is the smallest span of…
In a recent paper, it has been shown the Schr\"{o}dinger equation for the three-dimensional harmonic oscillator can be simplified through the use of an isometric conformal transformation. Here, it is demonstrated that the same…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
Modifications of Heisenberg's uncertainty relations have been proposed in the literature which imply a minimum position uncertainty. We study the low energy effects of the new physics responsible for this by examining the consequent change…
New time dependent Wigner functions for the quantum harmonic oscillator have been obtained in this work. The Moyal equation for the harmonic oscillator has been presented as the wave equation of a 2D membrane in the phase plane. The values…
We discuss factorization of the hypergeometric-type difference equations on the uniform lattices and show how one can construct a dynamical algebra, which corresponds to each of these equations. Some examples are exhibited, in particular,…