- #1

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## Homework Statement

The problem, along with a solution, is attached as an image file.

## Homework Equations

## The Attempt at a Solution

I have done the problem which was very straight forward. One simply had to look up the R

_{n,l}and then plug in the appropriate quantum numbers. Since for a given n, there are n-1 values of l, there are two corresponding radial functions R

_{2,0}and R

_{2,1}for the n=2 state. So the probability density which is [tex]\left|R\right|^{2}[/tex] is the sum of the probability of being in the l=0 state and probability of being in the l=1 state. Because the problem does not indicate the state of the initial wave function, we don't know the coefficients of R

_{2,0}and R

_{2,1}so my TA writes that we should assume they are equally probable. But what I don't understand is why in his probability density function he writes a 1/4 in front of the l=0 function and a 3/4 in front of the l=1 function. Where did these values come from? I'm posting here instead of asking my TA because I have a midterm tomorrow morning and I won't get a response from my TA in time if I were to email him now.

Thanks