Related papers: Exact Solutions of the two-dimensional Schr\"{o}di…
We present the exact and iterative solutions of the radial Schr\"{o}dinger equation for a class of potential, $V(r)=\frac{A}{r^{2}}-\frac{B}{r}+Cr^{\kappa}$, for various values of $\kappa$ from -2 to 2, for any $n$ and $l$ quantum states by…
In this paper, we provide the two-body exact solutions of two dimensional (2D) Schr\"{o}dinger equation with isotropic $\pm 1/r^3$ interactions. Analytic quantum defect theory are constructed base on these solutions and are applied to…
We obtain exact solutions of Dirac equation at zero kinetic energy for radial power-law relativistic potentials. It turns out that these are the relativistic extension of a subclass of exact solutions of Schrodinger equation with two-term…
We apply a simple transformation method to construct a set of new exactly solvable potentials (ESP) which gives rise to bound state solution of $D$-dimensional Schr\"odinger equation. The important property of such exactly solvable quantum…
We present, for the first time, exact solutions for the Schr\"{o}dinger equation in Moon and Spencer's toroidal coordinates, and in the electromagnetic toroidal--poloidal coordinate systems. Curiously, both systems present a fractional…
We propose a new method to obtain approximate solutions for the Schr\"{o}dinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows in many cases to find analytical…
Exact solvability (ES) of one-dimensional quantum potentials $V(x)$ is a vague concept. We propose that beyond its most conventional range the ES status should be attributed also to many less common interaction models for which the wave…
For any arbitrary values of $n$ and $l$ quantum numbers, we present a simple exact analytical solution of the $D$-dimensional ($D\geq 2$) hyperradial Schr% \"{o}dinger equation with the Kratzer and the modified Kratzer potentials within the…
Using the method of shape invariant potentials, a number of exact solutions of one dimensional effective mass Schrodinger equation are obtained. The solutions with equi-spaced spectrum are discussed in detail.
The problem of a fermion subject to a general scalar potential in a two-dimensional world is mapped into a Sturm-Liouville problem for nonzero eigenenergies. The searching for possible bounded solutions is done in the circumstance of…
Previously we found a unique quantum system with a positive gauge-invariant Weyl-Stratonovich quasi-probability density function which can be defined by the so-called {\guillemotleft}quadratic funnel{\guillemotright} potential [Phys. Rev. A…
We relax the regularity condition on potentials of the Schr\"odinger equation in uniqueness results on the inverse boundary value problem which were recently proved in [11] and [5].
In this paper, we establish various maximal principles and develop the direct moving planes and sliding methods for equations involving the physically interesting (nonlocal) pseudo-relativistic Schr\"{o}dinger operators…
A study is undertaken to investigate an analytical solution for the N-dimensional Schr\"{o}dinger equation with the Morse potential based on the Laplace transformation method. The results show that in the Pekeris approximation, the radial…
Recently was introduced in the literature a procedure to obtain ans\"atze, free of parameters, for the eigenfunctions of the time-independent Schr\"odinger equation with symmetric convex potential. In the present work, we test this…
Considering symmetric strictly convex potentials, a local relationship is inferred from the virial theorem, based on which a real log-concave function can be constructed. Using this as a weight function and in such a way that the virial…
We show that the Riccati form of the Schrodinger equation can be reformulated in terms of two linear equations depending on an arbitrary function G. When $G$ and the potential are polynomials, the solutions of these two equations are entire…
In this paper, we study the Schr\"odinger equation with a new quasi-exactly solvable double-well potential. Exact expressions for the energies, the corresponding wave functions and the allowed values of the potential parameters are obtained…
Using first and second order supersymmetry formalism we obtain a class of exactly solvable potentials subject to moving boundary conditions.
New exact analytical bound-state solutions of the radial Dirac equation in 3+1 dimensions for two sets of couplings and radial potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the…