4) A particle in the harmonic oscillator potential has the initial wave function P(x,0) = 1(x) = A(16(X) + 41(x)) for some constant A, where the 1 (x) are the time-independent harmonic oscillator eigenfunctions a. Normalize (x). Recall that the eigenfunctions satisfy 4,* (x) Wm(x) dx = om -oo Answer: A = V/2 b. Write the expressions for P(x, t) and | I(x, t) |2 Use the explicit form of the eigenfunctions given at the end of this Assignment. Also, 1 given E = n+ 2 ) ho, we can use for the time-dependent exponents: Eo E = and = 2 2