Title:
Tutorial example - hydrogen atom in polar coordinates
The purpose of this exercise is to
(1) see the advantage of flexible discretization for the H-atom
[TASK] vary the radial basis, study effect of the polExp on the accuracy
# the tricky thing is the long-range nature of the Coulomb potential
# it is good to have an infinitely extended discretiation to capture higher lying bound states
Axis: name, nCoefficients, lower end, upper end, functions, order
Rn, 20, 0., 10., polynomial,10
Rn, 20, 10., Infty, polExp[0.5]
Phi, 1,
Eta, 3, -1, 1, assocLegendre{Phi}
# NOTE: for simplicity, we calculate only m=0 states
# switching from the Harmonic oscillator to Coulomb is easy, isn't it?
Operator: hamiltonian
1/2<>-<1/Q><1><1>
# compute a few eigenvalues of the field free system
Eigen: select=SmallReal[7]
# put a 2d plot to files
Plot: axis,points,lowerBound,upperBound
Rn,101,0.,20.
Eta,31,-1.,1.