相关论文: The two-dimensional hydrogen atom revisited

An analytical perturbative method is suggested for solving the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0 in two dimensions where {\psi} vanishes on an irregular closed curve. We can thus find the energy levels of a quantum…

We consider the Schr\"odinger equation for hydrogen-like atom with Coulomb potential and non-point ball nucleus. The eigenvalues and eigenfunctions of the operator given by an arbitrary rotation-invariant boundary value problem on the…

Consider the problem: why does the bound state spectrum $E(n) < 0$, of hydrogen atom Hamiltonian $H$ have more degenerate eigenstates than those required by rotational symmetry? The answer is well known and was demonstrated by Pauli. It is…

Being comparable in quantum systems makes it possible for spaces with varying dimensions to attribute each other using special conversions can attribute schrodinger equation with like-hydrogen atom potential in defined dimensions to a…

The paper is continuation of [6] where we have discussed some classical and quantization problems of rigid bodies of infinitesimal size moving in Riemannian spaces. Strictly speaking, we have considered oscillatory dynamical models on…

The Schrodinger equation for stationary states is studied in a central potential V(r) proportional to the inverse power of r of degree beta in an arbitrary number of spatial dimensions. The presence of a single term in the potential makes…

It is shown that the Schrodinger equation for a large family of pairs of two-dimensional quantum potentials possess wavefuctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to…

We study periodic orbits in the spatial rotating Kepler problem from a symplectic-topological perspective. Our first main result provides a complete classification of these orbits via a natural parametrization of the space of Kepler orbits,…

The term describing the coupling between total angular momentum and energy-momentum in the hydrogen atom is isolated from the radial Dirac equation and used to replace the corresponding orbital angular momentum coupling term in the radial…

A two-dimensional hydrogen atom offers a promising alternative for describing the quantum interaction between an electron and a proton in the presence of a straight cosmic string. Reducing the hydrogen atom to two dimensions enhances its…

The relativistic equivalent of the Schr\"odinger equation for a two particle bound state having the total angular momentum $S$ is written in the form of a Lorentz covariant set of equations (p_1^mu+p_2^mu+Omega^mu)Psi(p_1,p_2;P)…

We study the most elementary aspects of harmonic analysis on a homogeneous space of a deformation of the two-dimensional Euclidean group, admitting generalizations to dimensions three and four, whose quantum parameter has the physical…

We note that presenting Hydrogen atom Schrodinger equation in the case of arbitrary dimensions require simultaneous modification of the Coulomb potential that only in three dimensions has the form Z/r . This was not done in a number of…

In this article we have developed a formalism to obtain the Schr$\ddot{\rm{o}}$dinger equation for a particle in a frame undergoing an uniform acceleration in an otherwise flat Minkowski space-time geometry. We have presented an exact…

Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schroedinger equation for them is solved by using a generalized series solution for the bound states (using the Froebenius method) and then an…

We study the exactly solvable quantum system of two particles confined in a three-dimensional harmonic trap and interacting via finite-range soft-core interaction by means of the separation of variables and ansatz method. Supposing the…

We present a definition of the two-sided inverse of position operator in general case of deformed Heisenberg algebra leading to minimal length. Energy spectrum and eigenfunctions in momentum space for 1D Coulomb-like potential in deformed…

A 3-dimensional non-commutative oscillator with no mass term but with a certain momentum-dependent potential admits a conserved Runge-Lenz vector, derived from the dual description in momentum space. The latter corresponds to a Dirac…

The question of whether hydrogen atoms can exist or not in spaces with a number of dimensions greater than 3 is revisited, considering higher dimensional Euclidean spaces. Previous results which lead to different answers to this question…

This paper investigates a two-dimensional Kemmer oscillator within relativistic quantum mechanics, incorporating minimal length and non-commutative phase space effects. We derive eigen solutions in configuration space $\{p\}$, examining the…