MATSLISE: Distorted Coulomb problems    

The Distorted Coulomb potential

Radial Schrödinger equations have the following form:

y'' = ( l*(l+1)/x^2 + V(x) - E)y, x > 0.

The potential is a distorted Coulomb potential, when

V(x) = S(x)/x + R(x),

where S(x) and R(x) are well behaved functions such that

            lim S(x) = S0,   lim S(x) = Sas,
             x->0             x->inf

            lim R(x) = R0,   lim R(x) = Ras,
             x->0             x->inf

where S0, Sas, R0 and Ras are constants. Specifically, it is assumed that around the origin S(x) and R(x) can be written in polynomial form and that some r_as does exist such that

Vas(x) = Sas/x + Ras

is a good approximation of V(x) for all r > r_as.

Solving the distorted Coulomb problem with MATSLISE

Figure 4: The problem-specification window for a Distorted Coulomb problem.

In order to specify the problem to solve, the user should provide some input:

Solving the distorted Coulomb problem means calculating the eigenvalues E and the associated eigenfunctions y. This can be done by clicking the construct-button.

References

[1] L. Gr. Ixaru, H. De Meyer and G. Vanden Berghe, Highly accurate eigenvalues for the distorted Coulomb potential, Phys. Rev. E 61 (2000) 3151-3159.


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