A Wavelet Solution For Time Independent Schrödinger Equation

Hossein Parsian

In this research work, We present a semi analytical solution for schrodinger equation. This method is based on generalized legendre wavelets and generalized operational matrices. Generalized legendre wavelets is a complete orthogonal set on the interval [0,s]. (s is a real arbitrary positive number.) The mother function of generalized legendre wavelets is generalized legendre functions. Generalized legendre function are an orthogonal set on the interval [-s,s]. The schrodinger equation is equal to a variational problem and we convert the variational problem to a non linear algebraic equations. From the solving of algebraic equation to get the eigenstates of schrodinger equation. We applied this method to one dimension non linear oscillator (V(x)=\\frac\{1\}\{n\}x^\{n\}, -\\infty < x < \\infty) and three dimensions non linear quantum oscillator (V(r)=\\frac\{1\}\{n\}r^\{n\}, 0