Derivation of Schrodinger eqn solutions.

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Zinc Potterman - 12 Jan 2005 22:40 GMT

I am reading An introduction to Quantum physics by French and Taylor which
is generally very clear.
However on page 207 there is (I believe) an important step missing in the
derivation of the the first three
spherically symmetric states of an electron in the Coulomb potential
V(r)=-Ze^2/r

I can figure out where the normalizing factor comes from and the decaying
exponential, but does anyone
know of a clear derivation of the polynomial part please.

Is it derived along similar lines to that of the one dimensional harmonic
oscillator using Hermite polynomials?
Zinc

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Jon Bell - 12 Jan 2005 23:36 GMT

> [...] derivation of the the first three
>spherically symmetric states of an electron in the Coulomb potential
[quoted text clipped - 3 lines]
>exponential, but does anyone
>know of a clear derivation of the polynomial part please.

If you're referring to the radial part of the wave function (in r), those
are "associated Laguerre polynomials." It's been a long time since I
studied this in detail, but I think you can find the derivation in
Merzbacher's "Quantum Mechanics" which was my textbook back then.

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Jon Bell <jtbellm4h@presby.edu> Presbyterian College
Dept. of Physics and Computer Science Clinton, South Carolina USA

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Natural Science Forum / Physics / Particle Physics / January 2005

Derivation of Schrodinger eqn solutions.