Question

8. One of your students tells you that a stationary state means the particle isn't moving. Explain what is wrong with this statement.

Answer 1

In the below pictures I have explained about the motion of the particle..And what actually happen in a stationary state..And clearly describe about stationary states..By giving an example...Read carefully...Also I have explained the condition of stationary states..

Hope you understand all the explanation....
stationary state: A stationary state is a quantum state with all observables independent of time This corresponds to a state with a single definite energy instead of a quantum superposition of different energies The solution of the times independent Schrodinger equation [- h^2/2 m nabla^2 + v (r)] Psi (r) = E Psi (r) can be written if the explicit form v(r) is known solution can be written as Psi_n (r, t) = Psi (r, 0) e^- i E n t/h where n = 1, 2, 3, .... \r\n This solution can be called stationary when Vertical-bar Psi_n (r, t) Vertical-bar ^2 = Psi*_n (r, t) Psi_n (r, t) = Psi*_n (r, theta) e^i E_n t/h Psi_n (r, 0) e^- i E_n t/h = Psi*_n (r, 0) Psi_n (r, 0) Vertical-bar Psi_n (r, t) Vertical-bar ^2 = Vertical-bar Psi_n (r, 0) Vertical-bar ^2 i.e., dependence on t has disappeared when a student is confused about the proper idea of stationary state and about the motion of particle, then we can get the proper idea about the motion of a particle when we study
hope i have cleared your confusion.