Variation Method

This chapter discusses variation method (an approximation, useful when Hamiltonian cannot be split suitably), for ground and excited states. Expectation value of H is to be minimized w.r.t. parameters of a trial wave function, guessed from intuition, physical insight, symmetries, boundary conditions, etc. It is applied to ground and excited states of linear harmonic oscillator and ground state of He-atom. Feynman’s theorem is introduced to calculate some matrix elements in a simple way, then applied to harmonic oscillator and H-atom. Also discussed use of trial wave function linear in variational parameters (useful in sophisticated numerical calculation of, for example, atomic and nuclear systems).