American Journal of Physics

A note on energy minimization and the quantum-mechanical virial theorem for the class of potentials V(x)=A‖x‖n

Harry A. Mavromatis

Published Dec 1, 1992• 1 citation

Abstract

It is pointed out that for the class of potentials V(x)=A‖x‖n, the quantum-mechanical virial theorem 〈φm‖T‖φm〉=(n/2)〈φm‖V‖φm〉 is in fact valid for any multiparameter trial wave function ψt=(1/√b)φt (x/b,a0̄,a1̄,...ar̄), where a0̄,a1̄,...ar̄, are dimensionless parameters, provided b is chosen to minimize 〈ψt‖T+V‖ψt〉, i.e., one requires (∂/∂b)[〈ψt‖T+V‖ψt〉]=0. A particular trial wave function of this type is used to illustrate this result.

DOI: 10.1119/1.16960

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