Rayleigh  Schrödinger perturbation series
for twodimensional anharmonic oscillator
w_{x}^{2} x^{2}/2 + w_{y}^{2} y^{2}/2 +
g^{1/2} x y^{2}
H = H_{0} + g^{1/2} x y^{2} 
Hamiltonian of the problem 
E(g) = E_{0} + E_{1} g + ...
+ E_{N} g^{N} 
Perturbation expansion of energy 
H_{0} = p_{x}^{2}/2 + p_{y}^{2}/2
+ w_{x}^{2} x^{2}/2 + w_{y}^{2} y^{2}/2 
Hamiltonian of harmonic oscillator 
E_{0} = (n_{x} + 1/2)w_{x}
+ (n_{y} + 1/2)w_{y} 
Unperturbed harmonicoscillator energy 
w_{x}, w_{y} 
Frequencies of normalmode vibrations 
g 
Small perturbation parameter 
n_{x}, n_{y} 
Harmonic oscillator quantum numbers 
N 
Order of perturbation theory 

Mathematica
program for this calculation
19
coefficients for
n_{x}=9, n_{y}=1,
w_{x}=1, w_{y}=11/10 in exact form
calculated earlier
4 coefficients for
n_{x}=9, n_{y}=1,
w_{x}=1 and arbitrary w_{y} in exact form
calculated earlier
110 coefficients for w_{x}=1, w_{y}=1.1, and
n_{x}=0, n_{x}=0,
n_{x}=0, n_{x}=1,
n_{x}=0, n_{x}=2,
n_{x}=0, n_{x}=4,
n_{x}=1, n_{x}=0,
n_{x}=1, n_{x}=2,
n_{x}=2, n_{x}=0,
n_{x}=2, n_{x}=1,
n_{x}=2, n_{x}=2,
n_{x}=3, n_{x}=0,
n_{x}=3, n_{x}=1,
n_{x}=4, n_{x}=0,
n_{x}=5, n_{x}=0,
calculated earlier
Online
calculation of Rayleigh  Schrödinger perturbation series
Online
calculations
Designed by A. Sergeev