Spectrum of Multipole Potential by Perturbation Theory in 3D Systems

Abstract

In this work, we calculate the spectrum of multipole potential by perturbation theory (monopole, dipole and quadrupole potential); for monopole case the potential equal Coulomb potential. We apply time independent perturbation theory to find analytical solutions of the Schrödinger equation in three dimensions in order to write corrections of the first three levels. For the dipole we find the first order correction is zero so we go to second order correction which. For quadrupole energy we get values of the same magnitude of dipole energy except when where the corrections of energy vanish.