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1. A particle in the infinite square well has the initial wave function L (2Ax, 0

1. A particle in the infinite square well has the initial wave function L (2Ax, 0

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Please assist with parts c, d and e.

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1. A particle in the infinite square well has the initial wave function 2Ax, L 0 <x < Ψ(χ,0) - L A(L – x), <xS L, 3 otherwise, for some constant A. This wave function is sketched below. V (x,0) 2AL 3 L (a) Determine the constant A by normalizing (x,0). (b) Find Y(x, t). (c) Calculate the probability that a measurement of the energy would yield the values (i) E, (ii) E2, and (iii) E3. (d) Calculate the average position, (x), of the particle at t = 0. (e) Calculate the average momentum, (p), of the particle at t = 0. (f) Calculate the average energy, (E), of the particle. (Note: 2n=112 sin? () = )
Transcribed Image Text:1. A particle in the infinite square well has the initial wave function 2Ax, L 0 <x < Ψ(χ,0) - L A(L – x), <xS L, 3 otherwise, for some constant A. This wave function is sketched below. V (x,0) 2AL 3 L (a) Determine the constant A by normalizing (x,0). (b) Find Y(x, t). (c) Calculate the probability that a measurement of the energy would yield the values (i) E, (ii) E2, and (iii) E3. (d) Calculate the average position, (x), of the particle at t = 0. (e) Calculate the average momentum, (p), of the particle at t = 0. (f) Calculate the average energy, (E), of the particle. (Note: 2n=112 sin? () = )
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