(a) Use this reursion formula, c_j+1 = (2(j+l+1-n)*c_j)/((j+1)(j+2l+2)), to confirm that when l=n-1 the radial wave function takes the form:

R_n,n-1 = (N_n)*r^(n-1)*e^(-r/(na))

(b) Calculate <r> and <r^2> for states psi_n,n-1,m.

Solution Preview

radial wave function stuff This question comes from the second edition of Griffiths' Introduction to Quantum Mechanics. It is question 4.46

(a) Use this recursion formula:
c_j+1 = (2(j+l+1-n)*c_j)/((j+1)(j+2l+2))
to confirm that when l=n-1 the radial wave function takes the form
R_n,n-1 = (N_n)*r^(n-1)*e^(-r/(na))

So the idea is to substitute l = n-1 ...

Solution Summary

This solution provides explanation for the student to be able to understand the problem and develop exact answer on their own.

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