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- 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
![displaymath11064](img288.gif)
- eigenvalues (energies) and eigenfunctions are expanded into power
series in
![eqnarray7540](img290.gif)
- eigenvalue problem
![displaymath11065](img291.gif)
- hierarchy of equations
![eqnarray7544](img292.gif)
- normalizations
![eqnarray7549](img293.gif)
- separable problems, second order ordinary differential equations (ODEs),
inhomogenous ODE
![displaymath11066](img294.gif)
- one solution
of the homogeneous equation
and another linearly independent solution
in
which the degree decreases
![eqnarray7557](img297.gif)
- particular solution of the inhomogenous equation, variation of parameters
![eqnarray7561](img298.gif)
- the general solution of the inhomogenous equation is
![displaymath11067](img299.gif)
- one particle Dirac equation
![displaymath11068](img300.gif)
- Hamiltonian
![eqnarray7569](img301.gif)
- for hydrogen-like atoms
![displaymath11069](img302.gif)
- two particle Dirac equation
- necessary algebraic operations
- indefinite integrals
- definite integrals
- pattern matching, zero recognition
- manipulation and simplification of large sums
Richard Liska