We present a new algebraic method for solving the inverse problem of quantum scattering theory based on Marchenko theory. applied triangular wave set equation kernel expansion in separable form. The form allows reduction to system linear equations. For zero orbital angular momentum, expression coefficients is obtained terms Fourier series function depending momentum $q$ and determined by data f...

We prove existence results for a stationary Schr{\"o}dinger equation with periodic magnetic potential satisfying local integrability condition on the whole space using critical value function.