## Angular Momentum Solution (Hydrogen Atom)

**a. ) Show that .**

**Solution:**

To obtain a solution to the equation derived in Problem (2), we assume a power series solution of the form:

.

Then

and

Substituting this to the equation solved in (2), we have

Since is linearly independent from all the rest, then each coefficient is equal to zero. That is,

.

**b.) Show that .**

**Solution:**

Since each coefficient is equal to zero, we find the coefficient of “ from the equation in Prob. (3). That is,

Changing :

.

Now, taking , we have

Finally,

.