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Problem 1.16 A particle is represented (at time t = 0) by the wave function %3D | A (a² – x²). -a

Problem 1.16 A particle is represented (at time t = 0) by the wave function %3D | A (a² – x²). -a

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Problem 1.16 A particle is represented (at time t = 0) by the wave function %3D | A (a² – x²). -a <x< +a, Y (x, 0) = 0, otherwise. (a) Determine the normalization constant A. (b) What is the expectation value of x? (c) What is the expectation value of p? (Note that you cannot get it from (p) = md (x) /dt. Why not?) (d) Find the expectation value of x². (e) Find the expectation value of p². (f) Find the uncertainty in x (ơx). (g) Find the uncertainty in p (op). (h) Check that your results are consistent with the uncertainty principle.
Transcribed Image Text:Problem 1.16 A particle is represented (at time t = 0) by the wave function %3D | A (a² – x²). -a <x< +a, Y (x, 0) = 0, otherwise. (a) Determine the normalization constant A. (b) What is the expectation value of x? (c) What is the expectation value of p? (Note that you cannot get it from (p) = md (x) /dt. Why not?) (d) Find the expectation value of x². (e) Find the expectation value of p². (f) Find the uncertainty in x (ơx). (g) Find the uncertainty in p (op). (h) Check that your results are consistent with the uncertainty principle.
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