- from T.C. Scott, R.A. Moore, M.B. Monagan, G.J. Fee,
E.R. Vrscay, J. of Comp. Phys., Vol. 87, No. 2, p.366-395, (1990).
- Rayleigh-Schrodinger perturbation theory
- Hamiltonian, solvable part and perturbative part

- eigenvalues (energies) and eigenfunctions are expanded into power
series in
- eigenvalue problem
- hierarchy of equations
- normalizations

- separable problems, second order ordinary differential equations (ODEs),
inhomogenous ODE
- one solution of the homogeneous equation
and another linearly independent solution in
which the degree decreases

- particular solution of the inhomogenous equation, variation of parameters
- the general solution of the inhomogenous equation is
- one particle Dirac equation
- Hamiltonian
- for hydrogen-like atoms

- two particle Dirac equation
- necessary algebraic operations
- indefinite integrals
- definite integrals
- pattern matching, zero recognition
- manipulation and simplification of large sums

- indefinite integrals

Richard Liska