New method of perturbation-theory calculation of the Stark effect for the ground state of hydrogen

Separation equations in parabolic coordinates are written in terms of the logarithmic derivative of the wave function. It is shown that for the ground state of the hydrogen Stark problem the $n$ th order of the perturbation expansion is a polynomial of order $n$ with integer coefficients. The energy coefficients. The energy coefficients, suitably defined, are integers and the calculation of the first 30 coefficients is listed.