Related papers: A study of the bound states for square potential w…
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,…
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…
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…
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…
Experts know that bound state energy eigenvalues of a potential well are poles of its transmission amplitude, $t(E)$. The textbooks do well by solving the bound states and scattering states separately, but the connection goes unheeded.…
We study the temporal formation of quantum mechanical bound states within a one-dimensional attractive square-well potential, by first solving the time-independent Schroedinger equation and then study a time dependent system with an…
We obtain eigenvalues and eigenfunctions of the Schr\"{o}dinger equation with a hyperbolic double-well potential. We consider exact polynomial solutions for some particular values of the potential-strength parameter and also numerical…
In modern fundamental theories there is consideration of higher dimensions, often in the context of what can be written as a Schr\"odinger equation. Thus, the energetics of bound states in different dimensions is of interest. By considering…
We present here a simple equation explicitly incorporating non-locality, which reproduces quantized energy levels of the bound states for the square well potentials. Introduction of this equation is motivated by studies of differential…
Four new exactly solvable, real and shape-invariant potentials associated with a position-dependent effective mass are generated within the concept of shape-invariant potentials using a specific ansatz for superpotential. The accompanying…
We analyze here the energy states and associated wave functions available to a particle acted upon by a delta function potential of arbitrary strength and sign and fixed anywhere within a one-dimensional infinite well. We consider how the…
A recursion technique of obtaining the asymptotical expansions for the bound-state energy eigenvalues of the radial Schr\"odinger equation with a position-dependent mass is presented. As an example of the application we calculate the energy…
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…
The effect of the uniform magnetic field on the electron in the spherically symmetric square-well potential is studied. A transcendental equation that determines the electron energy spectrum is derived. The approximate value of the lowest…
By using a point canonical transformation starting from the constant-mass Schr\"odinger equation for the Morse potential, it is shown that a semi-infinite quantum well model with a non-rectangular profile associated with a…
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 ${8 m}{w^2} / h^2$,…
We propose an experiential formula for the calculation of the energy eigenvalues of a particle moving in a one-dimension finite-deep square well potential after some physical considerations. This formula shows a simple relation between the…
We consider an unusual singular position=dependent-mass particle in an infinite potential well. The corresponding Hamiltonian is mapped through a point-canonical-transformation and an explicit correspondence between the target Hamiltonian…
We determine approximate eigenvalues and eigenfunctions shapes for bound states in the $3D$ shallow spherical ultrarelativistic well. Existence thresholds for the ground state and first excited states are identified, both in the purely…