Franz Schwabl Quantum Mechanics 4th Edit · Problem 2.7

One-Dimensional Problems

Physics — Quantum Mechanics · time-evolution-superposition-stationary-states

Problem

Let ψa(x)\psi_a(x) and ψb(x)\psi_b(x) be two orthonormal solutions of the time independent Schr\"odinger equation for a given potential with energy eigenvalues EaE_a and EbE_b. At the time t=0t=0, suppose that the system is in the state ψ(x,t=0)=12(ψa(x)+ψb(x)) .\psi(x,t=0) = \frac{1}{\sqrt{2}}\left(\psi_a(x) + \psi_b(x)\right)\,. Discuss the probability density at a later time tt.

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