Suppose you are given a problem involving an electron in a wire and you solve the time independent Schr¨odinger equation (TISE) to ?nd ?(x) for a particular energy level E. Write down the expression for ?(x, t) in terms of ?(x) and time t.
a. How would the wave function of the electron behave as a function of time?
b. How would the probability density for the electron behave as a function of time?
c. What is actually time-independent and what is time-dependent?