ESTIMATION OF GROUND-STATE ENERGY OF PARTICLE IN 1-D POTENTIAL WELL- VARIATION METHOD

Quantum mechanics provides approximate methods like perturbation and Variation methods to solve the one electron or many electron systems. The variation method is employed to solve the problem of particle in one dimensional potential well. The exact value of ground state energy (GSE) of particle in –D potential well and form of normalized wave function was calculated. The suitable trial wavefunctions are decided after some cumbersome calculations. Starting with these trail wavefunctions the expressions for expectation values of Hamiltonian () are obtained. The computer programs are designed to solve the tedious integrals in the expressions for Hamiltonian. The GSE of each trail wavefunction and values of variational parameter ( are obtained. The values of GSE with exact value are then discussed how one can approaches towards the exact wavefunction and GSE