Stuck on most of these questions, any help with them, even an outline of how to answer them, would be greatly appreciate

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Stuck on most of these questions, any help with them, even an
outline of how to answer them, would be greatly appreciated.

Stuck On Most Of These Questions Any Help With Them Even An Outline Of How To Answer Them Would Be Greatly Appreciate 1 (137.14 KiB) Viewed 167 times

Part III: Long Answer Questions Instructions: You must answer all the questions in this Part. Please clearly show the working for these problems in your answer booklet. (a) Consider a quantum particle of mass m trapped in one dimension in an infinite square well of width a. At time t = 0 the state of the particle is given by: 1 |v, t = 0): (1) + Ai (2) (2) √3 where [n) are the normalized solutions to the time independent Schrödinger equa- tion with position space representation ₁ (x) = (x|n) = √sin (7x). (i) Determine the real positive constant A. (ii) Determine (H) at t = 0 with H the Hamiltonian operator. (iii) Give the wave-function as a function of time. (iv) Will (H) change with time? (explain your answer) (v) Give the probability that a measurement of the energy conducted at t = 0 will will yield (H). (vi) Calculate (p) as a function of time. (b) In the following three tasks, consider a hydrogen atom in the ground state. (i) Give the possible and m quantum numbers. (ii) Give the angular wave-function. (iii) Calculate the expectation value of the electron's position. =