In a modern physics course you learn that a hydrogen atom has allowed energies -13.6/n^2 eV, where n ...

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In a modern physics course you learn that a hydrogen atom has allowed energies -13.6/n^2 eV, where n = 1, 2, 3, ..., which are the solutions of the time-independent Schrodinger equation. The wavefunction of the state with energy -13.6 eV is denoted psi_1(r), and that of the state with energy -13.6/4 eV is psi_2(r); both are normalized. (a) Suppose that at time t = 0 the system's wavefunction is Psi(r, 0) = psi_1(r). (i) What is Psi(r, t) at some later time t? (ii) Calculate the probability densities at t = 0 and at time t. Compare the two and comment on your results. (b) Repeat parts (a)(i) and (a)(ii) for Psi(r, 0) = psi_2(r). (c) Now suppose that at t = 0 the wavefunction is Psi(r, 0) = sqrt(1/5) psi_1(r) + sqrt(4/5) psi_2(r). (i) What is Psi(r, t) at some later time t? (ii) Calculate the probability densities at time 0 and at time t using your result from part (c)(i), and comment on your result.