Related papers: Numerical solutions for a two dimensional quantum …
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…
The aims of the reported work are to provide new insights into the quantum dot optical properties confined in an inverse of a quadratic Hellmann potential. The Schr\"odinger equation is solved using the Nikiforov-Uvarov (NU) method, in…
New solutions for second-order intertwining relations in two-dimensional SUSY QM are found via the repeated use of the first order supersymmetrical transformations with intermediate constant unitary rotation. Potentials obtained by this…
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),…
The matrix Numerov method provides an efficient framework for solving the time-independent Schr\"odinger equation as a matrix eigenvalue problem. However, for singular potentials such as the Coulomb interaction, the expected fourth-order…
In this paper we present an algebraic study concerning the general second order linear differential equation with polynomial coefficients. By means of Kovacic's algorithm and asymptotic iteration method we find a degree independent…
By converting the rectangular basis potential V(x,y) into the form as V(r)+V(r, phi) described by the pseudo central plus noncentral potential, particular solutions of the two dimensional Schrodinger equation in plane-polar coordinates have…
We present a procedure to solve the Schroedinger equation of two interacting electrons in a quantum dot in the presence of an external magnetic field within the context of quasi-exactly-solvable spectral problems. We show that the…
A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the…
We derive five classes of quantum time-dependent two-state models solvable in terms of the double confluent Heun functions, five other classes solvable in terms of the biconfluent Heun functions, and a class solvable in terms of the…
We construct new solutions in series of confluent hypergeometric functions for the confluent Heun equation (CHE). Some of these solutions are applied to the one-dimensional stationary Schr\"{o}dinger equation with hyperbolic and…
We propose an analytical approach for computing the eigenspectrum and corresponding eigenstates of a hyperbolic double well potential of arbitrary height or width, which goes beyond the usual techniques applied to quasi-exactly solvable…
A procedure is proposed to construct solutions of the double confluent Heun equation with a determinate behaviour at the singular points. The connection factors are expressed as quotients of Wronskians of the involved solutions. Asymptotic…
In this article we are interested for the numerical study of nonlinear eigenvalue problems. We begin with a review of theoretical results obtained by functional analysis methods, especially for the Schrodinger pencils. Some recall are given…
The Schroedinger equation with one and two dimensional potentials are solved in the frame work of the sl(2) Lie algebra. Eigenfunctions of the Schroedinger equation for various asymmetric double-well potentials have been determined and the…
In a previous article we have shown how one can employ Artificial Neural Networks (ANNs) in order to solve non-homogeneous ordinary and partial differential equations. In the present work we consider the solution of eigenvalue problems for…
Generalizations of the complex number system underlying the mathematical formulation of quantum mechanics have been known for some time, but the use of the commutative ring of bicomplex numbers for that purpose is relatively new. This paper…
Since the advent of quantum mechanics different approaches to find analytical solutions of the Schr\"odinger equation have been successfully developed. Here we follow and generalize the approach pioneered by Natanzon and others by which the…
Exactly solvable models play an extremely important role in many fields of quantum physics. In this study, the Schr\"{o}dinger equation is applied for a solution of a two--dimensional (2D) problem for two particles interacting via Kratzer,…
The supersymmetric approach in the form of second order intertwining relations is used to prove the exact solvability of two-dimensional Schrodinger equation with generalized two-dimensional Morse potential for $a_0=-1/2$. This…