L*Yem (0,6) = NYem+1 (0,6), where N is a number, (a) show that |Nf = (L*Ycm, L*Yam). (b) and hence using the hermiticity of L, and L, show that Then using the equality L-L* = L² – L? – ħL,, and the eigenvalue equations show that N= h/(e+1+m) ({ – m).
L*Yem (0,6) = NYem+1 (0,6), where N is a number, (a) show that |Nf = (L*Ycm, L*Yam). (b) and hence using the hermiticity of L, and L, show that Then using the equality L-L* = L² – L? – ħL,, and the eigenvalue equations show that N= h/(e+1+m) ({ – m).
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Transcribed Image Text:If
L*Ytm (0,¢) = NYtm+1 (0,9),
where N is a number,
(a) show that
|N = (L+Yem, L*Yem).
(b) and hence using the hermiticity of L, and Ly show that
|N
(Yem, L-L*Yem) -
Then using the equality
L-L* = L² – L? – ħL,,
and the eigenvalue equations show that
N = h/(e+1+m) (l – m).
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