# 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