PHYS 041C Lecture Notes - Lecture 1: Uncertainty Principle, Hidden Variable Theory, Self-Adjoint Operator
Document Summary
This may be something you think you now understand or something that you still don"t understand after reading the book. As to why we can subtract inside the parentheses. The hidden variable theory, and the spooky distance was confusing to understand (the logic behind it). Two eigenvalues for the parity operator: and. Are the eigenfunctions for a given hermitian operator orthogonal for all. Yes, the eigenfunctions in question are orthogonal for all hermitian operators, since any hermitian operation produces a distinct eigenvalue. Yes, after commuting, they have a set of shared eigenfunctions (or eigenfunctions that they have in common). First, it contradicts our answer above; if they don"t commute, they can"t have a set of eigenfunctions in common. It does not vary with time (it is constant), since equation 5. 73 below is independent of time, and only varies with motion.
