Related papers: A systematic study on the exact solution of the po…
With the consideration of spherical symmetry for the potential and mass function, one-dimensional solutions of non-relativistic Schrodinger equations with spatially varying effective mass are successfully extended to arbitrary dimensions…
The complete solutions of the Schr\"odinger equation for a particle with time-dependent mass moving in a time-dependent linear potential are presented. One solution is based on the wave function of the plane wave, and the other is with the…
Solutions of time-independent Schrodinger equation for potentials periodic in space satisfy Bloch theorem. The theorem has been used to obtain solutions of the Schrodinger equation for periodic systems by expanding them in terms of plane…
The effective mass one-dimensional Schr\"odinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also…
The Cauchy problem for the Schr\"odinger equations is studied with time-dependent potentials growing polynomially in the spatial direction. First the existence and the uniqueness of solutions are shown in the weighted Sobolev spaces. In…
Point canonical transformation (PCT) has been used to find out new exactly solvable potentials in the position-dependent mass (PDM) framework. We solve $1$-D Schr\"{o}dinger equation in the PDM framework by considering two different fairly…
The general solution of SUSY intertwining relations of first order for two-dimensional Schr\"odinger operators with position-dependent (effective) mass is built in terms of four arbitrary functions. The procedure of separation of variables…
We analyze a general family of position-dependent mass quantum Hamiltonians which are not self-adjoint and include, as particular cases, some Hamiltonians obtained in phenomenological approaches to condensed matter physics. We build a…
We solve the parametric generalized effective Schr\"odinger equation with a specific choice of posi-tion-dependent mass function and Morse oscillator potential by means of the Nikiforov-Uvarov (NU) method combined with the Pekeris…
Evaluation of a product integral with values in the Lie group SU(1,1) yields the explicit solution to the impedance form of the Schr\"odinger equation. Explicit formulas for the transmission coefficient and $S$-matrix of the classical…
Using first and second order supersymmetry formalism we obtain a class of exactly solvable potentials subject to moving boundary conditions.
We build an efficient and unitary (hence stable) method for the solution of the semi-classical Schr\"odinger equation subject with explicitly time-dependent potentials. The method is based on a combination of the Zassenhaus decomposition…
Some exactly solvable potentials in the position dependent mass background are generated whose bound states are given in terms of Laguerre- or Jacobi-type $X_1$ exceptional orthogonal polynomials. These potentials are shown to be shape…
We provide a squeeze-like transformation that allows one to remove a position dependent mass from the Hamiltonian. Methods to solve the Schr\"{o}dinger equation may then be applied to find the respective eigenvalues and eigenfunctions. As…
The kinetic energy operator with position-dependent-mass in plane polar coordinates is obtained. The separability of the corresponding Schr\"odinger equation is discussed. A hypothetical toy model is reported and two exactly solvable…
An algorithm for the numerical solution of the Schr\"odinger equation in the case of a time dependent potential is proposed. Our simple modification upgrades the well known method of Koonin while negligibly increasing the computing time. In…
Extending the point canonical transformation approach in a manner distinct from the previous ones, we propose a unified approach of generating potentials of all classes having non-constant masses.
We propose an exact method for solving a one-dimensional Schr\"odinger equation. An arbitrary potential is represented by the collection of short-width potentials. For building the collection scheme, a new solvable potential is introduced.…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
In a previous paper$^1$, submitted to Journal of Physics A -- we presented an infinite class of potentials for which the radial Schr\"odinger equation at zero energy can be solved explicitely. For part of them, the angular momentum must be…