Related papers: Bound states in a semi-infinite square potential w…
A square potential well with position-dependent mass is studied for bound states. Applying appropriate matching conditions, a transcendental equation is derived for the energy eigenvalues. Numerical results are presented graphically and the…
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…
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…
One of the most widely problem studied in quantum mechanics is of an infinite square-well potential. In a minimal-length scenario its study requires additional care because the boundary conditions at the walls of the well are not well…
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…
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…
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…
We present a solution of the quantum mechanics problem of the allowable energy levels of a bound particle in a one-dimensional finite square well. The method is a geometric-analytic technique utilizing the conformal mapping $w \to z = w…
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…
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…
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 ${8 m}{w^2} / h^2$,…
Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all…
The Schrodinger equation for a particle moving in a square well potential with BenDaniel - Duke boundary conditions is solved. Using algebraic approximations for trigonometric functions, the transcendental equations of the bound states…
We consider the quantum problem of a particle in either a spherical box or a finite spherical well confined by a circular cone with an apex angle $2\theta_0$ emanating from the center of the sphere, with $0<\theta_0<\pi$. This non-central…
An infinite sequence of potential well functions is considered. A numerical method is used for the Schr$\ddot{\text{o}}$dinger equation to obtain the energy eigenvalue spectra for a number of these potential well functions. The results for…
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…
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…
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…
An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…
Highly accurate closed-form approximations are given for the ground state and first excited state wavefunctions and energies for a nonrelativistic particle in a one-dimensional double square well potential with a square barrier in between…