Suppose a one-dimensional infinite square well potential of width as shown below:
V(x)
Consider a particle with mass confined in the potential, which has the initial wavefunction of Ψ(x,0) = A√2/L sin(πx/L) for 0 ≤ x ≤ L.
(a) Find the energy eigenvalues and corresponding eigenstates that satisfy the boundary conditions. (6 pts)
(b) Determine and find Ψ(x,t) at time t. (10 pts)
(c) What is the expectation value of the energy? (ptS)
(d) Calculate the standard deviation of the momentum Δp. If L is reduced or increased, how does Δp change? Explain this from the uncertainty principle. (10 pts)