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

arXiv:1408.6139

Treatment of $N$-dimensional Schrödinger equation for anharmonic potential via Laplace transform

Tapas Das

Published Aug 25, 2014• 2 citations
arXivHTMLPDF

Abstract

First time anharmonic potential $V(r)=ar^2+br-\frac{c}{r} \,,(a>0) $ is examined for $N$-dimensional Schrödinger equation via Laplace transformation method. In transformed space, the behavior of the Laplace transform at the singular point of the differential equation is used to study the eigenfunctions and the energy eigenvalues.The results are easy to derive and identical with those obtained by other methods.

DOI
10.48550/arxiv.1408.6139

Related papers

Exact Analytical Solution of the N -Dimensional Radial Schrödinger Equation with Pseudoharmonic Potential via Laplace Transform Approach

Tapas Das, Altuğ Arda

The second-order N -dimensional Schrödinger equation with pseudoharmonic potential is reduced to a first-order differential equation by using the Laplace transform approach and exact bound state solutions are obtained using convolution theorem. Some special cases are verified and variations of energy eigenvalues En as a function of dimension N are furnished. To give an extra depth of this paper, the present approach is also briefly investigated for generalized Morse potential as an example.

arXiv:1308.5295•Advances in High Energy Physics•Jan 1, 2015•32 citations

Solution of the Schrödinger equation for a particular form of Morse potential using the Laplace transform

M. Zarezadeh, Mohammad Kazem Tavassoly

In this paper, we have solved the Schrödinger equation for a particular kind of Morse potential and find its normalized eigenfunctions and eigenvalues, exactly. Our work is based on the Laplace transform technique which reduces the second-order differential equation to a first-order.

Chinese Physics C•Apr 1, 2013•12 citations

Solution of Schrödinger equation by Laplace transform

M. J. Englefield

Laplace transform techniques for solving differential equations do not seem to have been directly applied to the Schrödinger equation in quantum mechanics. This may be because the Laplace transform of a wave function, in contrast to the Fourier transform, has no direct physical significance. However, this paper will show that scattering phase shifts and bound state energies can be determined from the singularities of the Laplace transform of the wave function. The Laplace transform method can thereby simplify calculations if the potential allows a straightforward solution of the transformed Schrödinger equation. Suitable cases are the Coulomb, oscillator and exponential potentials and the Yamaguchi separable non-local potential.

Journal of the Australian Mathematical Society•Aug 1, 1968•14 citations

Exact solutions of N -dimensional harmonic oscillator via Laplace transformation

Chen Gang

The N -dimensional Schrödinger equation for the harmonic oscillator is reduced to a first-order differential equation in terms of the Laplace transformation and the exact bound state solutions are derived. It is shown that this method of solving Schrödinger equation may serve as a substitute for the standard functional, analytical approach also in lower dimensions.

Chinese Physics•May 3, 2005•40 citations

The solution of D-dimensional Schrodinger equation for potential V(r)=ar2+br+cr-1+dr-2+er-3+fr-4 by using Ansatz method

Kristiana Nathalia Wea, Suparmi Suparmi, C. Cari +1 more

The solution of the Schrodinger equation with the physical potential is important part in quantum mechanics. The anharmonic potential is one of the physical potential that is interesting to be explored. Many methods have been developed to solve the Schrodinger equation. The Ansatz wave function method is one of the many methods that used to solve the Schrodinger equation. The Ansatz wave function method was used to solve the radial part of Schrodinger Equation. In this study we present the solution of the radial part Schrodinger equation in D-dimensional system with potential V(r)=ar2+br+cr-1+dr-2+er-3+fr-4. The important part in Ansatz wave function method is to determine the wave function Ansatz corresponding to the shape of the anharmonic potential that used. The Ansatz wave function determined by using supersymmetric approximation. By substituting the wave function Ansatz into Schrodinger equation and using algebraic we obtain the radial eigenfunction and the energy, and then the eigenfunction visualized.

AIP conference proceedings•Jan 1, 2017•1 citation

Bound state solutions of the one-dimensional Schrdinger equation for the harmonic oscillator via the Laplace transform

Zidong Chen

AbstrcatThe second-order one-dimensional Schrdinger differential equation for the harmonic oscillator is reduced to a first-order differential equation by means of the Laplace transform,and then,its solutions are obtained by means of directly making use of an integral.The energy spectrum is derived from the condition that the wave functions must be single-valued.The required eigenfunctions are obtained by applying the expansions of series and inverse Laplace transform.

College Physics•Jan 1, 2005•0 citations
Treatment of NNN-dimensional Schrödinger equation for anharmonic potential via Laplace transform
First time anharmonic potential V(r)=ar2+br−cr ,(a>0)V(r)=ar^2+br-\frac{c}{r} \,,(a>0) V(r)=ar2+br−rc​,(a>0) is examined for NNN-dimensional Schrödinger equation via Laplace transformation method. In transformed space, the behavior of the Laplace transform at the singular point of the differential equation is used to study the eigenfunctions and the energy eigenvalues.The results are easy to derive and identical with those obtained by other methods.
Laplace transform techniques for solving differential equations do not seem to have been directly applied to the Schrödinger equation in quantum mechanics. This may be because the Laplace transform of a wave function, in contrast to the Fourier transform, has no direct physical significance. However, this paper will show that scattering phase shifts and bound state energies can be determined from the singularities of the Laplace transform of the wave function. The Laplace transform method can thereby simplify calculations if the potential allows a straightforward solution of the transformed Schrödinger equation. Suitable cases are the Coulomb, oscillator and exponential potentials and the Yamaguchi separable non-local potential.
The solution of the Schrodinger equation with the physical potential is important part in quantum mechanics. The anharmonic potential is one of the physical potential that is interesting to be explored. Many methods have been developed to solve the Schrodinger equation. The Ansatz wave function method is one of the many methods that used to solve the Schrodinger equation. The Ansatz wave function method was used to solve the radial part of Schrodinger Equation. In this study we present the solution of the radial part Schrodinger equation in D-dimensional system with potential V(r)=ar2+br+cr-1+dr-2+er-3+fr-4. The important part in Ansatz wave function method is to determine the wave function Ansatz corresponding to the shape of the anharmonic potential that used. The Ansatz wave function determined by using supersymmetric approximation. By substituting the wave function Ansatz into Schrodinger equation and using algebraic we obtain the radial eigenfunction and the energy, and then the eigenfunction visualized.