Related papers: Solution of the quantum finite square well problem…
The bound state energies of a 1-dimensional finite quantum square well (FSW) can be determined using a geometric method, involving a smooth mapping between two copies of the complex plane. The method allows one to identify particular…
The finite square potential well is a staple problem in introductory quantum mechanics. There is an extensive literature on the determination of the allowed energies, which requires the solution of a transcendental equation by numerical,…
Within the framework of fractional quantum mechanics, an exact solution has been found for the energy spectrum of a quantum particle confined in a quantum well - a symmetric one-dimensional finite potential well. A simple graphical…
We give a lower bound for the energy of a quantum particle in the infinite square well. We show that the bound is exact and identify the well-known element that fulfils the equality. Our approach is not directly dependent on the…
A chart for the quantum mechanics of a particle of mass $m$ in a one-dimensional potential well of width $w$ and depth $V_0$ is derived. The chart is obtained by normalizing energy and potential through multiplication by ${8 m}{w^2} / h^2$,…
The one-dimensional infinite square well is the simplest solution of quantum mechanics, and consequently one of the most important. In this article, we provide this solution using the real Hilbert space approach to quaternic quantum…
Using a recent reformulation of quantum mechanics where the potential function is not required, we are able to obtain the energy spectrum and wave function associated with the infinite square well analytically. Therefore, this work…
The eigenvalue equations for the energy of bound states of a particle in a square well are solved, and the exact solutions are obtained, as power series. Accurate analytical approximate solutions are also given. The application of these…
From a careful study of the transcendental equations fulfilled by the bound state energies of a free particle in a quantum well, cylindrical wire or spherical dot with finite potential barrier, we have derived analytical expressions of…
This paper present how to solve the problem of cylindrical quantum wells with potential energy different from zero and with singularity of the energy on the axis of the cylinder. The solution to the problem was obtained using methods of…
Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of…
Analytical calculations based on a Landau Level (LL) picture are reported for a many-electron system moving in an interface (with a finite-width Quantum Well (QW)) and in the presence of an external perpendicular magnetic field. They lead…
We use the discrete approach to solve the Schr\"odinger as well as the Bloch equations for a free particle and the quantum gas of free particles embedded in an infinite quantum well with the finite width. We obtain the expressions of energy…
In the present paper a method of finding the dynamics of the Wigner function of a particle in an infinite quantum well is developed. Starting with the problem of a reflection from an impenetrable wall, the obtained solution is then…
We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schr\"odinger models with energy-dependent potentials, conventional Schr\"odinger…
A method for determination of bound state energies for an asymmetric quantum well with an arbitrary shape of the bottom is suggested. It is shown that how the equation determining the energy levels can be easily derived if one knows the…
We introduce a numerical method to obtain approximate eigenvalues for some problems of Sturm-Liouville type. As an application, we consider an infinite square well in one dimension in which the mass is a function of the position. Two…
We extend the standard treatment of the asymmetric infinite square well to include solutions that have zero curvature over part of the well. This type of solution, both within the specific context of the asymmetric infinite square well and…
There are various types of infinite potential well problems occurring in elementary quantum mechanics formalism. The infinite square well (one dimensional), cubical box and, spherical well are quite common in textbooks. In this paper, we…
We introduce two potentials explicitly given by the Lambert-W function for which the exact solution of the one-dimensional stationary Schr\"odinger equation is written through the first derivative of a double-confluent Heun function. One of…