Solution of the R, , and Equations

The solution of Eq. (4-36) is similar to that of the particle in a ring problem of Section 2-6. The normalized solutions are 

As shown in Section 2-6, the constant m must be an integer if 4 is to be a single-valued function. 

There is great similarity between the mathematical techniques used in solving the R and 0 equations and those used to solve the one-dimensional harmonic oscillator problem of Chapter 3. Hence, we will only suimnarize the steps involved in these solutions and make a few remarks about the results. More detailed treatments are presented in many texts.  

Change the variable to obtain a more convenient form for the differential equation. 

Express the solution as a power series and obtain a recursion relation. 

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