would someone mind explaining why, in general, degenerate (quantum) states are not orthogonal?
Degenerate states form a whole subspace. The linear superposition of two degenerate states is again a state with the same eigenvalue. So your question is equivalent to:
can someone explain me why all vectors aren't orthogonal ?
However, it is always possible to choose an orthogonal basis in this subspace, and those eigenvectors ARE orthogonal.
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