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Old Jun 6th 2018, 04:09 PM   #11
Pmb
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I can't see his justification of Eq. [2.63] on page 47. I know its true but long ago forgot why and I can't see Griffith writing anything to justify it. Help/thoughts?
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Old Jun 8th 2018, 08:54 AM   #12
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Originally Posted by Pmb View Post
I can't see his justification of Eq. [2.63] on page 47. I know its true but long ago forgot why and I can't see Griffith writing anything to justify it. Help/thoughts?
I think it's considered as a consequence of Eq. 2.61, which shows that the next/previous wave function in the ladder is obtained by applying the operator and renormalising. Therefore, the proportionality constant, $\displaystyle c_n$, is just the inverse of $\displaystyle A_n$, repurposed for the algebraic method. Considering how $\displaystyle c_n$ is linked to $\displaystyle A_n$, it is unsurprising, then, that the result is a square root of a factorial.
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