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My sense was that it was Pauli, but I can't seem to find any evidence to support this.

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The solution is in Schroedinger's first paper on wave mechanics --- but believe it was Herman Weyl who did the Laguerre Polynomial math. Weyl lived almost next door to Schrodinger and was Schroedinger's wifes lover at the time.

A good account is in "Schrödinger: Life and Thought" by Walter Moore.

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