The wavefunctions and energy eigenvalues of the Schrodinger Equation for different potentials due to the virial theorem

Abstract

The derivation of the virial theorem is presented both in classical and quantum mechanical approach. The kinetic energy and potential energy of the mechanical energy is converted to each other due to the virial theorem. Some of the different potentials are considered. For some of these potentials, the wavefunctions and energy eigenvalues of the Schrödinger Equation are derived.