Consider 2 energy eigenfunctions u1(x) and u2(x) corresponding to the eigenvalues E1 and E2 respectively, and they are different from each other. Assume that the eigenfunctions vanish outside the regions I and II, respectively. Show that : a) If a particle is initially in region I, it will stay there. b) If the particle is in the state with the wavefunction Ψ(x, 0) = (1/sqrt(2))*(u1+u2), its probability density is independent of time.
Consider 2 energy eigenfunctions u1(x) and u2(x) corresponding to the eigenvalues E1 and E2 respectively, and they are different from each other. Assume that the eigenfunctions vanish outside the regions I and II, respectively. Show that : a) If a particle is initially in region I, it will stay there. b) If the particle is in the state with the wavefunction Ψ(x, 0) = (1/sqrt(2))*(u1+u2), its probability density is independent of time.
Related questions
Question
Consider 2 energy eigenfunctions u1(x) and u2(x) corresponding to the eigenvalues E1 and E2 respectively, and they are different from each other. Assume that the eigenfunctions vanish outside the regions I and II, respectively.
Show that :
a) If a particle is initially in region I, it will stay there.
b) If the particle is in the state with the wavefunction Ψ(x, 0) = (1/sqrt(2))*(u1+u2), its probability density is independent of time.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
