Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics Letters A

A new approach to solve the one-dimensional Schrödinger equation using a wavefunction potential

Sergio A. Hojman, Felipe A. Asenjo

Published Sep 28, 2020• 8 citations
Publisher
DOI
10.1016/j.physleta.2020.126913

Related papers

A new approach to solving the Schrödinger equation using wavefunction potentials in two and three dimensions

Valentina A. Villaflor, V. Alejandro Muñoz-Mosqueira, Sergio A. Hojman

The European Physical Journal Plus•May 7, 2024•1 citation

A new approach to solving the Schrödinger equation

Sergio A. Hojman, Felipe A. Asenjo

A new approach to find exact solutions to one--dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions having vanishing and non--vanishing Bohm potentials. For most of the potentials, no solutions to the Schrödinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some quantum, such as accelerated Airy wavefunctions, are due to the presence of non--vanishing Bohm potentials. New examples of this kind are found and discussed.

arXiv:2007.02182•Jul 4, 2020•1 citation

Decoupling the One Dimensional Dirac Equations With a Scalar Potential

Francesco R. Ruggeri

In a previous note (1), it was noted one could write a solution of the bound state Schrodinger equation as W(x)=Wo(x)Dn(x) where W(x) is the wavefunction and Wo(x), the ground state wavefunction. Inserting into the Schrodinger equation one may obtain the Schrodinger equation for Wo(x) and an equation coupling Wo(x) and Dn(x). In this note, we suggest such an approach may be applied to the one dimensional bound Dirac equations. This allows one to obtain decoupled equations for u1(x) and v1(x) where u(x)=uo(x)u1(x) and v(x)=v1(x)vo(x) are the full solutions. Thus, if one is able to obtain a solution for uo(x) and vo(x) by inspection, the decoupled equations allow one to find the general solution. We apply this approach to the case of a scalar potential g|x|. The Dirac problem for this potential has been solved in the literature (2) with decoupling occurring through the taking of spatial derivatives. Here we wish to suggest a general method.

•Aug 10, 2019•0 citations

Convenient numerical technique for solving the one-dimensional Schrödinger equation for bound states

Patrick J. Cooney, E. P. Kanter, Z. Vager

American Journal of Physics•Jan 1, 1981•24 citations

Dirac equation with position-dependent effective mass and solvable potentials in the Schrödinger equation

H. Panahi, Zahra Bakhshi

We study the one-dimensional non-Hermitian imaginary potential with a real energy spectrum in the framework of the position-dependent effective mass Dirac equation. The Dirac equation is mapped into the exactly solvable Schrödinger-like equation endowed with position-dependent effective mass that we present a new procedure to solve it. The point canonical transformation in non-relativistic quantum mechanics is applied as an algebraic method to obtain the mass function and then by using the obtained mass function, the imaginary potential can be obtained. The spinor wavefunctions for some of the obtained electrostatic potentials are given in terms of orthogonal polynomials. We also obtain the relativistic bound state spectrum for each case in terms of the bound state spectrum of the solvable potentials.

Journal of Physics A Mathematical and Theoretical•Apr 4, 2011•18 citations

Solution of the Schrödinger Equation in One Dimension

S. Brandt, Hans Dieter Dahmen

Springer eBooks•Jan 1, 2001•0 citations
A new approach to find exact solutions to one--dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions having vanishing and non--vanishing Bohm potentials. For most of the potentials, no solutions to the Schrödinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some quantum, such as accelerated Airy wavefunctions, are due to the presence of non--vanishing Bohm potentials. New examples of this kind are found and discussed.
In a previous note (1), it was noted one could write a solution of the bound state Schrodinger equation as W(x)=Wo(x)Dn(x) where W(x) is the wavefunction and Wo(x), the ground state wavefunction. Inserting into the Schrodinger equation one may obtain the Schrodinger equation for Wo(x) and an equation coupling Wo(x) and Dn(x). In this note, we suggest such an approach may be applied to the one dimensional bound Dirac equations. This allows one to obtain decoupled equations for u1(x) and v1(x) where u(x)=uo(x)u1(x) and v(x)=v1(x)vo(x) are the full solutions. Thus, if one is able to obtain a solution for uo(x) and vo(x) by inspection, the decoupled equations allow one to find the general solution. We apply this approach to the case of a scalar potential g|x|. The Dirac problem for this potential has been solved in the literature (2) with decoupling occurring through the taking of spatial derivatives. Here we wish to suggest a general method.
We study the one-dimensional non-Hermitian imaginary potential with a real energy spectrum in the framework of the position-dependent effective mass Dirac equation. The Dirac equation is mapped into the exactly solvable Schrödinger-like equation endowed with position-dependent effective mass that we present a new procedure to solve it. The point canonical transformation in non-relativistic quantum mechanics is applied as an algebraic method to obtain the mass function and then by using the obtained mass function, the imaginary potential can be obtained. The spinor wavefunctions for some of the obtained electrostatic potentials are given in terms of orthogonal polynomials. We also obtain the relativistic bound state spectrum for each case in terms of the bound state spectrum of the solvable potentials.