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Journal of Physics A Mathematical and General

A simple interpolation method for extracting quantal information from partially known potentials

M. Casas, F. Garcías, Angelo Plastino

Published Jan 21, 1994• 0 citations
Publisher

Abstract

From the sole knowledge of the numerical values of the potential V(x) at a finite number of points we are able to construct the potential as a function of the coordinate and infer approximate wavefunctions without in any way (numerically) dealing with Schrodinger's equation.
DOI
10.1088/0305-4470/27/2/032

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We solve the Schrodinger equation analytically for systems whose potentials have a certain time-dependence (which is monotonously decreasing) and general coordinate-dependences.Only a few time-dependent systems have been reported to be analytically solved whose potentials are constant, linear, and quadratic functions of coordinate with arbitrary time-dependences.From a different perspective, we focus on the time-dependent systems whose potentials are monotonously decreasing functions of time with arbitrary coordinate dependences.Time-dependent potential of any coordinate-dependence can be handled analytically by transforming it to a time-independent potential of known solutions if its time-dependence is monotonously decreasing.We do this by a unitary transformation of the wavefunction and variable transformations to change the Schrodinger equation to be time-independent in new variables.These variables are then determined by solving a set of simple differential equations.This way we are able to find and to obtain analytical solutions for time-dependent potentials which we mention above.