scholarly journals Mathematical analysis of the dimensional scaling technique for the Schrödinger equation with power-law potentials

2010 ◽  
Vol 51 (12) ◽  
pp. 123508 ◽  
Author(s):  
Zhonghai Ding ◽  
Goong Chen ◽  
Chang-Shou Lin
Keyword(s):  
Schrödinger Equation ◽  
Power Law ◽  
Mathematical Analysis ◽  
Schrodinger Equation ◽  
Scaling Technique ◽  
Dimensional Scaling

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

2002 ◽  
Vol 17 (24) ◽  
pp. 1567-1573
Author(s):  
AXEL SCHULZE-HALBERG
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Large Class ◽  
Power Law ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Stationary Schrödinger Equation ◽  
Dependent Mass

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.

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