A particle is represented (at time t = 0) by the wave function Y(x,0) = √ B (b² − 3x²), −b ≤ x ≤ +b - 0, otherwise (a) Determine the normalization constant B. (b) What is the expectation value of x ? (c) What is the expectation value of p? And find (p) = md(x)/dt , then check between the results if they are same or not. (d) Find the expectation value of x². (e) Find the expectation value of p². (f) Find the uncertainty in x (x). (g) Find the uncertainty in p (p). (h) Check that your results are consistent with the uncertainty principle.
A particle is represented (at time t = 0) by the wave function Y(x,0) = √ B (b² − 3x²), −b ≤ x ≤ +b - 0, otherwise (a) Determine the normalization constant B. (b) What is the expectation value of x ? (c) What is the expectation value of p? And find (p) = md(x)/dt , then check between the results if they are same or not. (d) Find the expectation value of x². (e) Find the expectation value of p². (f) Find the uncertainty in x (x). (g) Find the uncertainty in p (p). (h) Check that your results are consistent with the uncertainty principle.
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Transcribed Image Text:A particle is represented (at time t = 0) by the wave function
Y(x,0) =
√ B (b² − 3x²), −b≤ x ≤ +b
0,
otherwise
(a) Determine the normalization constant B.
(b) What is the expectation value of x ?
(c) What is the expectation value of p? And find (p) = md(x)/dt
, then check between the results if they are same or not.
(d) Find the expectation value of x².
(e) Find the expectation value of p².
(f) Find the uncertainty in x (x).
(g) Find the uncertainty in p (p).
(h) Check that your results are consistent with the uncertainty principle.
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