At time t = 0 an electron is in the Ground State energy of an infinite square we

Question

At time t = 0 an electron is in the Ground State energy of an infinite square well. Assume that, unless a measurement is made the particle is isolated and obeys time-evolution according to the Schrodinger equation. At time t = T the position of the electron is measured to be a/2. Assume the wavefunction at time t =T is symmetric about x = a/2. If one were to measure the energy immediately after t = T what possible values could be obtained? A. Only the ground state energy B. Any of the possible energies of the infinite square well where n is 1, 3, 5..., etc. C. Any of the possible energies of the infinite square well where n is 2, 4, 6..., etc. D. Any of the possible energies of the infinite square well Psi_n (x) = Squareroot 2/a sin (n pi/a x) E_n = h^2 n^2 pi^2/2ma^2

Explanation / Answer

Ans is D. Any of the energies of the well.

These states are stationery states. Unless perturbed by an external force they will remain at that state like electrons in stationery states of H atom. They can go to any suitable Eigen state when are disturbed during the process of measurement by supplying energy to it.

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