Rayleigh - Schrödinger perturbation series
for two-dimensional anharmonic oscillator
wx2 x2/2 + wy2 y2/2 + g1/2 x y2

Enter oscillator quantum numbers nx =
ny =
0, 1, 2, 3, ...
Enter frequencies of vibrations wx =
wy =
Integer, rational or floating-point numbers
Enter order of perturbation theory N = 1, 2, 3, ...
Enter working precision ndigits = 16 for standard, 17, 18, 19, ... for multiple precision,
or 0 for exact symbolic calculations
Default response

H = H0 + g1/2 x y2 Hamiltonian of the problem
E(g) = E0 + E1 g + ... + EN gN Perturbation expansion of energy
H0 = px2/2 + py2/2 + wx2 x2/2 + wy2 y2/2 Hamiltonian of harmonic oscillator
E0 = (nx + 1/2)wx + (ny + 1/2)wy Unperturbed harmonic-oscillator energy
wx, wy Frequencies of normal-mode vibrations
g Small perturbation parameter
nx, ny Harmonic oscillator quantum numbers
N Order of perturbation theory

Mathematica program for this calculation

19 coefficients for nx=9, ny=1, wx=1, wy=11/10 in exact form calculated earlier

4 coefficients for nx=9, ny=1, wx=1 and arbitrary wy in exact form calculated earlier

110 coefficients for wx=1, wy=1.1, and nx=0, nx=0, nx=0, nx=1, nx=0, nx=2, nx=0, nx=4, nx=1, nx=0, nx=1, nx=2, nx=2, nx=0, nx=2, nx=1, nx=2, nx=2, nx=3, nx=0, nx=3, nx=1, nx=4, nx=0, nx=5, nx=0, calculated earlier

RSPTexpansionOn-line calculation of Rayleigh - Schrödinger perturbation series

Online calculations

Designed by A. Sergeev