Hi, i am having trouble understanding a section of a QM course concerning degenerate eigenstates.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that some operator B is compatible with A (so A and B have a common eigenbasis). My notes say that this means that some r and r+pi/2 give eigenstates of both A and B in the form |a(r)> = (cos(r)|a1> + sin(r)|a2>) where |a1> and |a2> are two orthogonal degenerate eigenstates of A. I don't understand why the eigenstates have this form?

It goes on to say that in order to find the appropriate value of r we must solve for the eigenvectors of:

<a1|B|a1> <a1|B|a2>

<a2|B|a1> <a2|B|a2>

I don't understand this either... what is the significance of the eigenvectors of this matrix? (i believe the eigenvalues are the quantised measurables of B)

Any help would really be appreciated, Thanks

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# Distinguishing between eigenstates

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