- Please Help Me Solve These Questions 1 (349.38 KiB) Viewed 27 times
Please help me solve these questions.
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answerhappygod
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Please help me solve these questions.
Please help me solve these questions.
(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: | V₁ t = 0) = -√3|1) + Ai |2) (2) where [n) are the normalized solutions to the time independent Schrödinger equa- tion with position space representation ₁ (x) = (x|n) = √²/sin (1x). n (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.
(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: | V₁ t = 0) = -√3|1) + Ai |2) (2) where [n) are the normalized solutions to the time independent Schrödinger equa- tion with position space representation ₁ (x) = (x|n) = √²/sin (1x). n (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.