The system is at the state of Φ=aY_11+bY_20 (a^2+b^2=1),please find the possible eigenfunctions of Lx and the relevant possibilities?(adsbygoogle = window.adsbygoogle || []).push({});

My solution: I have attempted to use the matrix mechanics to work out the exercise,but I should work out a 8-order matrix.

Firstly I use the Fmn=〈m︳F|n〉to work out the matrix Lx in the Hilbert space of Lz or

L^2,then use the Time-independent Schrodinger Equation ,namely (Lx)mn ψ=Lx ψ ,to work out its eigenvector|ψn〉.At last ,I use the 〈Φ︳ψn〉,we can figure out probability of the related eigenvalue.I have tried to solute it in this way ,but in the process ,we should work out a 8-order matrix .It is too difficult to deal with it .

Are there someone have easier way to solute the question?

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# Homework Help: A question about hydrogen atom

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