Calculate Rayleigh - Schrodinger perturbation series for superposition of the Coulomb and Yukawa potentials

Hamiltonian for this screened Coulomb potential known as Hellmann potential has the form:
H = p²/2 - 1/r + g[1-exp(-delta r)]/r, where g is a mixing parameter and delta is an inverse screening radius considered as a small perturbation parameter.

The energy is expanded in powers of delta:
E(delta) = E₀ + E₁ delta + ... + E_N delta^N, where
      E₀ = -1/(2 n²) is unperturbed Coulomb energy,
      n and l are the principal and azimuthal oscillator quantum numbers, and
      N is the order of perturbation theory.

Download a text of the Mathematica program that is used for this calculation.

This program can be easily modified for a screened Coulomb potential of a general form
-1/r + v₁ delta + v₂ delta² r + v₃ delta³ r² + ... + v_N delta^N r^N-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.

Directory of Sergeev's files Designed by A. Sergeev

Сайт создан в системе uCoz

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