Construction of a trial function in the variational procedure of quantum mechanics

R. Kh. Sabirov

Moscow State Pedagogical University, 119882 Moscow, Russia

(Submitted 26 May 1995)

Zh. ~ks~. Teor. Fiz. 108, 1179-1 185 (October 1995)


Abstract

A form of variational method for calculating the ground-state energy of a quantum system is considered. The method is based on a prescription for the systematic construction of a trial variational function at each step in the calculation of the ground-state energy; the prescription improves the previous result. In each step of the calculation, it is straightforward to obtain the new variational function. The method is tested in two nontrivial problems. Good agreement between the calculated ground-state energy and its exact value is found. The transformation of the wave function in the transition from one step of the calculation to the next is traced. It is shown that as the number of steps in the calculation increases the variational wave function reproduces with ever greater accuracy the characteristic features inherent in the exact wave function of the ground state.


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