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 (<H>) 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.