Related papers: Symmetric Fermi-type potential
We identify a symmetry that enforces every symmetric model to have a Fermi surface. These symmetry-enforced Fermi surfaces are realizations of a powerful form of symmetry-enforced gaplessness. The symmetry we construct exists in quantum…
We present a semiclassical study of level widths for a class of one-dimensional potentials in the presence of an ohmic environment. Employing an expression for the dipole matrix element in terms of the Fourier transform of the classical…
For any central potential V in D dimensions, the angular Schroedinger equation remains the same and defines the so called hyperspherical harmonics. For non-central models, the situation is more complicated. We contemplate two examples in…
We analyze the one dimensional scattering produced by all variations of the P\"oschl-Teller potential, i.e., potential well, low and high barriers. We show that the P\"oschl-Teller well and low barrier potentials have no resonance poles,…
We study the radial Schr\"{o}dinger equation for a particle of mass $m$ in the field of the inverse-square potential $\alpha/r^{2}$ in the medium-weak-coupling region, i.e., with $-1/4\leq2m\alpha/\hbar^{2}\leq3/4$. By using the…
In this paper we obtain approximate bound state solutions of $N$-dimensional time independent fractional Schr\"{o}dinger equation for generalised pseudoharmonic potential which has the form…
Using the formalism of supersymmetric quantum mechanics, we obtain a large number of new analytically solvable one-dimensional periodic potentials and study their properties. More specifically, the supersymmetric partners of the Lame…
In this letter, we consider a Schrodinger equation for a well potential with varying width. We solve one dimensional time-dependent Schrodinger equation subject to time-dependent boundary conditions for a spinless particle inside infinite…
A simple formalism for exploring quantum scattering and possible bound states in an arbitrary symmetric and localized potential in a unified way is presented. The symmetric square barrier and well potentials are used for illustrating the…
In this work, aiming to solve numerically the Schr\"odinger equation with a Dirac delta function potential, we use the Numerov method to solve the time independent 1D-Schr\"odinger equation with potentials of the form V(x) + deltap(x),…
In view of the obstacles encountered in any attempts to solve the Minkowski-space Bethe-Salpeter equation for bound states of two fermions, we study the possibility to model the bound-state features, at least at a qualitative level, by a…
The classical Schr\"odinger equation with a harmonic trap potential $V(x)=|x|^2$, describing the quantum harmonic oscillator, has been studied quite extensively in the last twenty years. Its ground states are bell-shaped and unique, among…
We investigate the approximate bound state solutions of the Schr\"odinger equation for the PT-/non-PT-symmetric and non Hermitian Hellmann potential. Exact energy eigenvalues and corresponding normalized wave functions are obtained.…
The Gross-Pitaevskii equation is solved by analytic methods for an external double-well potential that is an infinite square well plus a $\delta$-function central barrier. We find solutions that have the symmetry of the non-interacting…
We perform the complete group classification in the class of cubic Schr\"odinger equations of the form $i\psi_t+\psi_{xx}+\psi^2\psi^*+V(t,x)\psi=0$ where $V$ is an arbitrary complex-valued potential depending on $t$ and $x$. We construct…
This paper concernes with the existence of heteroclinic solutions for the following class of elliptic equations $$ -\Delta{u}+A(\epsilon x, y)V'(u)=0, \quad \mbox{in} \quad \Omega, $$ where $\epsilon >0$, $\Omega=\R \times \D$ is an…
A new form to construct complex superpotentials that produce real energy spectra in supersymmetric quantum mechanics is presented. This is based on the relation between the nonlinear Ermakov equation and a second order differential equation…
Bound states generated by K coupled PT-symmetric square wells are studied in a series of models where the Hamiltonians are assumed $R-$pseudo-Hermitian and $R^2-$symmetric. Specific rotation-like generalized parities $R$ are considered such…
The ring-shaped Hartmann potential $ V = \eta \sigma^{2} \epsilon_{0} \left( \frac{2 a_{0}}{r} - \frac{\eta a_{0}^{2}}{r^{2} sin^{2} \theta} \right) $ was introduced in quantum chemistry to describe ring-shaped molecules like benzene. In…
We present analytical formulas for the vacuum-polarization Uehling potential in the case where the finite size of the nucleus is modeled by a Fermi charge distribution. Using a Sommerfeld-type development, the potential is expressed in…