Rayleigh - Schrödinger perturbation series
for superposition of the Coulomb and Yukawa potentials
-1/r + g[1-exp(-delta r)]/r

Enter the principal and
azimuthal quantum numbers
n =
l =
0 for the ground or 1, 2, 3, ... for excited states
0 for S-state or 1, 2, ..., n-1 for P, D, ... states
Enter mixing parameter g = Integer, rational or floating-point. One for Yukawa potential.
Enter zero (0) to leave g unevaluated.
Enter order of perturbation theory N = 1, 2, 3, ...
Default response

H = H0 + g[1-exp(-delta r)]/r Hamiltonian of the problem
E(delta) = E0 + E1 delta + ... + EN deltaN Perturbation expansion of energy
H0 = p2/2 - 1/r Hamiltonian of hydrogen atom
E0 = -1/(2 n2) Coulomb energy (Rydberg formula)
n, l Principal and azimuthal quantum numbers
g Mixing parameter
delta Inverse screening radius
N Order of perturbation theory

Mathematica program for this calculation. This program could be easily modified for a screened Coulomb potential of a more general form
-1/r + v1 delta + v2 delta2 r + v3 delta3 r2 + ... + vN deltaN rN-1.

102 - 110 coefficients for 1s (the ground state, n=1, l=0), 2s (n=2, l=0), and 2p (n=2, l=1) states in exact form calculated earlier

150 coefficients for the ground state of Yukawa potential calculated earlier

RSPTexpansionOn-line calculation of Rayleigh - Schrödinger perturbation series

Online calculations

Designed by A. Sergeev