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please show all work,thank you for helping. In quantum mechanics physical observ

ID: 3895838 • Letter: P

Question

please show all work,thank you for helping.

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

please show all work,thank you for helping. In quantum mechanics physical observ