Related papers: Exact solutions for the D-dimensional spherical is…
The exact two-particle energy eigenstates in a generic asymmetric rectangular box with periodic boundary conditions in all three directions are studied. Their relation with the elastic scattering phases of the two particles in the continuum…
Recently, in arXiv:1105.2298 [hep-th], we have estimated the energy radiated in the head-on collision of two equal D-dimensional Aichelburg-Sexl shock waves, for even D, by solving perturbatively, to first order, the Einstein equations in…
The problem of the harmonic oscillator with a centrally located delta function potential can be exactly solved in one dimension where the eigenfunctions are expressed as superpositions of the Hermite polynomials or as confluent…
The factorization method of Schrodinger shows us how to determine the energy eigenstates without needing to determine the wavefunctions in position or momentum space. A strategy to convert the energy eigenstates to wavefunctions is well…
The Schr\"odinger equation is thoroughly analysed for the isotropic oscillator in the three-dimensional space of constant positive curvature in the spherical and cylindrical systems of coordinates. The expansion coefficients between the…
We study the three-body Coulomb problem in two dimensions and show how to calculate very accurately its quantum properties. The use of a convenient set of coordinates makes it possible to write the Schr\"{o}dinger equation only using…
We use the optimized trigonometric finite basis method to find energy eigenvalues and eigenfunctions of the time-independent Schrodinger equation with high accuracy. We apply this method to the quartic anharmonic oscillator and the harmonic…
It is shown that the eigenvalue problem for the Hamiltonians of the standard form, $H=p^2/(2m)+V(x)$, is equivalent to the classical dynamical equation for certain harmonic oscillators with time-dependent frequency. This is another…
We consider N atoms trapped in an isotropic harmonic potential, with s-wave interactions of infinite scattering length. In the zero-range limit, we obtain several exact analytical results: mapping between the trapped problem and the…
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,…
In this paper, the $d$-dimensional quantum harmonic oscillator with a pseudo-differential time quasi-periodic perturbation \begin{equation}\label{0} \text{i}\dot{\psi}=(-\Delta+V(x)+\epsilon W(\omega t,x,-\text{i}\nabla))\psi,\ \ \ \ \…
We consider Schr\"{o}dinger equations with linearly energy-depending potentials which are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under…
As a generalization and extension of our previous paper {\it J. Phys. A: Math. Theor. 53 055302} \cite{AME2020}, in this work we study a quantum 4-body system in $\mathbb{R}^d$ ($d\geq 3$) with quadratic and sextic pairwise potentials in…
In this paper, we investigate a two dimensional isotropic harmonic oscillator on a time-dependent spherical background. The effect of the background can be represented as a minimally coupled field to the oscillator's Hamiltonian. For a…
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…
We investigate a $D$ dimensional generalization of the Schroedinger-Newton equations, which purport to describe quantum state reduction as resulting from gravitational effects. For a single particle, the system is a combination of the…
The energy levels of quantum systems are determined by quantization conditions. For one-dimensional anharmonic oscillators, one can transform the Schrodinger equation into a Riccati form, i.e., in terms of the logarithmic derivative of the…
Eigenmodes of electromagnetic field with perfectly conducting or infinitely permeable conditions on the boundary of a D-dimensional spherically symmetric cavity is derived explicitly. It is shown that there are (D-2) polarizations for TE…
We consider the radial Schr\" odinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of…
Heavy quarkonia, Bc-meson, and CS-meson masses are calculated within the framework of the N-dimensional radial Schrodinger equation. The Cornell potential is extended by including the harmonic oscillator potential. The energy eigenvalues…