Simple variational approach to the one-dimensional Schrodinger equation

Charles K. Manka

John R. Merrill, Gregory P. Hughes

Kálmán Varga, Joseph A. Driscoll

Carlos Esebbag, J Nunez, Angel Ricardo Plastino +1 more

An extremely simple (approximate) variational method for the study of the eigensolutions of the one-dimensional Schrodinger equation is introduced, based upon the idea of employing scaled eigenstates of the harmonic oscillator as generating functions for the generator coordinate method. The approach is successfully applied to a variety of situations.

Elso Drigo Filho, Regina Maria Ricotta, Natália Fávaro Ribeiro

Carl A. Kocher

When does the Schrödinger equation have bound-state solutions? This question is pursued by a variational method with simple trial wave functions. An arbitrary one- or two-dimensional attractive potential is shown to have at least one discrete energy level, and estimates of the binding energy are obtained for shallow potential wells. In other problems, sufficient conditions are established for the existence of bound states.