The Central Potential
a) By writing grad^ in terms of r, theta and phi show that this can be written as
(b) Writing shi = R Y show that Y must satisfy L^2 Y = c Y where c is a constant, and where
(c) Writing R = f(r)/r, show that f(r) satisfies the equation
(d) This is of exactly the same form as a 1-D time independent Schrodinger equation with V replaced by V + c/2mr^2. So can we conclude that the spectrum in the original 3D problem is the same as for this 1D problem?
Following is the text part of the 5-page solution. Please see the attached file for complete solution. Equations, diagrams, graphs and special characters will not appear here. Thank you for using Brainmass.
Solution is very detailed. Every step of the solution has been shown clearly. I have used equation editor to type in equations. Hence, the typing and clarity of the solution is similar to what you would find in a textbook.