- #1

Master J

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The Hydrogen Atom wave function.

With the substitution u(r) = r.R(r)

p=kr

We get a simplified version: d^2u/dp^2 = [1 - (p_0)/p + l(l + 1)/(p^2) ].u

Im sure some of you have seen that before.

Now, in the limit, p goes to infinity, I understand that we get u = A.exp[-p], but in the limit that p goes to 0, the answer is:

d^2u/dp^2 = [l(l + 1)/(p^2)].u

I don't get where that comes from. Surely the terms with p at the bottom explode and become infinite??

With the substitution u(r) = r.R(r)

p=kr

We get a simplified version: d^2u/dp^2 = [1 - (p_0)/p + l(l + 1)/(p^2) ].u

Im sure some of you have seen that before.

Now, in the limit, p goes to infinity, I understand that we get u = A.exp[-p], but in the limit that p goes to 0, the answer is:

d^2u/dp^2 = [l(l + 1)/(p^2)].u

I don't get where that comes from. Surely the terms with p at the bottom explode and become infinite??

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