I need help with the process for each part, the solution is given. Spherically s

Question

I need help with the process for each part, the solution is given.

Spherically symmetric solution to Schrodinger equation For hydrogen atom 1/r d2/dr2 (r ) = -8m pi2/h2 [E + e02/r) Psi Psi = Psi(r) Psi = energy state of a particle (wave soln) r = radices of hydrogen atom Let r = h2/4pi2 m alpha20 alpha E = 2pi2 m alpha04/h2 E Initial eqn - d2(p psi)/d p2 = 1 (epsilon + 2/p)p psi part (1) let f= p psi d2f/dp2 = -(epsilon + 2/p)f solution part (2) let f(p) = e-alpha p g (p) d2g/dp2 = 2 alpha dg/dp + (2/p + epsilon + alpha2)g=0 leftarrow solution let alpha2 = -epsilon and simplify d2g/dp 2alpha dg/dp + 2/p g = 0 leftarrow solution show that for large k(k-500) your coefficient ak+1 = (2alpha)k/K!

Explanation / Answer

You can refer this website for complete explanations

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html

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