I believe that this is similar to the proof of schrodinger equation to obtain quantum numbers, however i cannot seem to understand the relationship between n, l and m:(adsbygoogle = window.adsbygoogle || []).push({});

I have attached a pdf file on partial differential equations and on page 5, i cannot seem to understand why it is +n^2 and l,m are negative?

Also, on page 6 it states 'Hence the sumis also a solution. Note ℓ and m do not have to be integers and so

the above need not be a discrete sum. Also note that if ℓ → 0, cosine is replaced

by 1 and sine by x.' why is sine replaced by x, shouldn't it disappear as it equals to 0 rather than being replaced by x?

My final query is about equation 1.28, how the superposition principle is applied? Does it just form linear equations of the solutions and why is the solution for equation 1.27 cosh and sinh whereas for the rest it isn't?

Thank you so much in advance , whoever can clear this for me

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# Cant understand similar proof Quantum numbers from PDE (pdf attachment!)

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