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solution for ode

Posted 10 years ago

the following ode appears in in the quantum mechanics of stark effect.can you obtain the solution and show it is related to associated laguerre polynomials. enter image description here

POSTED BY: HARIKRISHNAN A
2 Replies

The Stark effect here evidently includes both linear (a x) and quadratic (e x^2) contributions. It is usually treated by perturbation theory. The Stark effect with just the linear contribution can be solved exactly in parabolic coordinates. The quadratic part can then be treated as a perturbation.

POSTED BY: S M Blinder

is there any way to solve it using frobenius power series method ??

POSTED BY: HARIKRISHNAN A
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