Related papers: Spherically symmetric potential in noncommutative …
We present a novel numerical method and algorithm for the solution of the 3D axially symmetric time-dependent Schr\"odinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent…
In this work, we present an exact analysis of two-dimensional noncommutative hydrogen atom. In this study, it is used the Levi-Civita transformation to perform the solution of the noncommutative Schr\"odinger equation for Coulomb potential.…
Interactions of noncommutative solitons in a modified U(n) sigma model in 2+1 dimensions can be analyzed exactly. Using an extension of the dressing method, we construct explicit time-dependent solutions of its noncommutative field equation…
An N-dimensional position-dependent mass Hamiltonian (depending on a parameter \lambda) formed by a curved kinetic term and an intrinsic oscillator potential is considered. It is shown that such a Hamiltonian is exactly solvable for any…
We extend here the canonical treatment of spherically symmetric (quantum) gravity to the most simple matter coupling, namely spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the…
We consider the defocusing nonlinear Schr{\"o}dinger equation in several space dimensions, in the presence of an external potential depending on only one space vari-able. This potential is bounded from below, and may grow arbitrarily fast…
A (p,q)-deformation of the Landau problem in a spherically symmetric harmonic potential is considered. The quantum spectrum as well as space noncommutativity are established, whether for the full Landau problem or its quantum Hall…
It has been suggested that the high symmetries in the Schr\"odinger equation with the Coulomb or harmonic oscillator potentials may remain in the corresponding relativistic Dirac equation. If the principle is correct, in the Dirac equation…
This article deals with a nonrelativistic quantum mechanical study of a charge-dyon system with the SU(2)--monopole in five dimensions. The Schr\"odinger equation for this system is separable in the hyperspherical and parabolic coordinates.…
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…
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…
A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…
We numerically simulate gravitational collapse in asymptotically anti-de Sitter spacetimes away from spherical symmetry. Starting from initial data sourced by a massless real scalar field, we solve the Einstein equations with a negative…
The construction of $\mathcal{PT}$-symmetric quantum electrodynamics is reviewed. In particular, the massless version of the theory in 1+1 dimensions (the Schwinger model) is solved. Difficulties with unitarity of the $S$-matrix are…
It is shown that the quantum Hamiltonian characterising a non-relativistic electron under the influence of an external spherical symmetric electromagnetic potential exhibits a supersymmetric structure. Both cases, spherical symmetric scalar…
Besides the standard quantum version of the Coulomb/Kepler problem, an alternative quantum model with not too dissimilar phenomenological (i.e., spectral and scattering) as well as mathematical (i.e., exact-solvability) properties may be…
In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with…
We study the scalar, conformally invariant wave equation on a four-dimensional Minkowski background in spherical symmetry, using a fully pseudospectral numerical scheme. Thereby, our main interest is in a suitable treatment of spatial…
Two new methods for investigation of two-dimensional quantum systems, whose Hamiltonians are not amenable to separation of variables, are proposed. 1)The first one - $SUSY-$ separation of variables - is based on the intertwining relations…
A new spherically-symmetric solution is determined in a noncompactified Kaluza-Klein theory in which a time character is ascribed to the fifth coordinate. This solution contains two independent parameters which are related with mass and…