Construction of A Trial Function In The Variational Procedure of Quantum Mechanics

A form of variational method for calculating the ground state energy of a quantum mechanical system is considered. The method is based on a systematic construction of a trial variational function at each step of the calculation of the ground state energy. The construction involves introducing more variational parameters to the trial wave function such that; the more variational parameters retained, the more accurate the calculated ground state energy. The method is tested using two different quantum mechanical systems. Good agreement between the calculated ground state energy and the corresponding exact value is found. The forms of the wave function in the transition from one step of the calculation to the next are also obtained