please show all work,thank you for helping. In quantum mechanics physical observ
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In quantum mechanics physical observables are given by eigenvalues of operators. Recall that we said that the separation constant in our solutions, E. was the energy of the particle. Show that E is the eigenvalue of the energy operator. That is, show that Psi(x, t) = E Psi (x, t) where Psi (x, t) is a separable wave-function Psi (x,t) = phi (x,t) = phi (x) (t) (Hint: we already solved for (t) in class.) Consider a traveling plane-wave solution in complex exponential form psi(x, t) = A0 exp[i(kx - wt)}. We know that for photons, their momentum is given by k. Show that k is an eigenvalue of the momentum operator. That is, show that psi (x, t) = k psi(x, t). Using the same wave-function as in part b), show that w is an eigenvalue of the energy operator. (Bv the way, recall that a photon's energy is given by hf = w.)Explanation / Answer
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