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 Research International

Reduction of Time‐Dependent Schrödinger Equations with Effective Mass to Stationary Schrödinger Equations

Axel Schulze‐Halberg

Published Dec 9, 2007• 2 citations
Publisher

Abstract

We introduce a class of potentials for which the time‐dependent Schrödinger equation with position‐dependent (effective) mass allows reduction to a stationary Schrödinger equation. This reduction is done by a particular point canonical transformation which preserves L2‐normalizability.
DOI
10.1155/2008/589269

Related papers

Form-Preserving Transformations of Time-Dependent Schrödinger Equation with Time- and Position-Dependent Mass

Axel Schulze‐Halberg

We study space-time transformations of the time-dependent Schrödinger equation (TDSE) with time- and position-dependent (effective) mass. We obtain the most general space-time transformation that maps such a TDSE onto another one of its kind. The transformed potential is given in explicit form.

Communications in Theoretical Physics•Apr 1, 2005•9 citations

Form-Preserving Transformations of Time-Dependent Schrōdinger Equation with Time- and Position-Dependent Mass

AxelSchulze-Halberg

We study space-time transformations of the time-dependent Schrōdinger equation (TDSE) with time- and position-dependent (effective) mass. We obtain the most general space-time transformation that maps such a TDSE onto another one of its kind. The transformed potential is given in explicit form.

理论物理通讯:英文版•Jan 1, 2005•0 citations

Effective Mass Schrodinger Equation for Exactly Solvable Class of One-Dimensional Potentials

Metin Aktaş, R. Sever

We deal with the exact solutions of Schrodinger equation characterized by position-dependent effective mass via point canonical transformations. The Morse, Poschl-Teller and Hulthen type potentials are considered respectively. With the choice of position-dependent mass forms, exactly solvable target potentials are constructed. Their energy of the bound states and corresponding wavefunctions are determined exactly.

arXiv:quant-ph/0608054•Aug 7, 2006•0 citations

Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

Axel Schulze‐Halberg

Abstract We study the time-dependent Schrödinger equation (TDSE) with an effective (position-dependent) mass, relevant in the context of transport phenomena in semiconductors. The most general form-preserving transformation between two TDSEs with different effective masses is derived. A condition guaranteeing the reality of the potential in the transformed TDSE is obtained. To ensure maximal generality, the mass in the TDSE is allowed to depend on time also.

Open Physics•Dec 1, 2005•15 citations

Exact Solutions of the Schrödinger Equation with Position-dependent Effective Mass via General Point Canonical Transformation

C. Tezcan, R. Sever

Journal of Mathematical Chemistry•Jun 12, 2006•49 citations

A METHOD OF GENERATING EXACT SOLUTIONS OF THE TIME-DEPENDENT SCHRÖDINGER EQUATION WITH TIME-DEPENDENT MASS

Axel Schulze‐Halberg

Extending the method presented in our previous paper,12 we map the time-dependent Schrödinger equation (TDSE) with time-dependent mass on a stationary Schrödinger equation for a nonconstant potential. On solving the latter, we can thus generate a large class of exact solutions of the original TDSE. Several examples are given, including potentials of power-law and modified Pöschl–Teller type.

Modern Physics Letters A•Aug 10, 2002•0 citations