A particle is represented (at time t=0) by the wave function -x¹) if- a ≤x≤a otherwise if. ¥(x,0) = {4(a* − xª) 0 a) Determine the normalization constant A b) What is the expectation value of x (at time t=0) c) What is the expectation value of p (at time t=0) d) Find the expectation value of x² e) Find the expectation value of p² f) Find the uncertainty in x (0) 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 -x¹) if- a ≤x≤a otherwise if. ¥(x,0) = {4(a* − xª) 0 a) Determine the normalization constant A b) What is the expectation value of x (at time t=0) c) What is the expectation value of p (at time t=0) d) Find the expectation value of x² e) Find the expectation value of p² f) Find the uncertainty in x (0) 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
-
¥(x,0) = {A(a¹ − x¹) if − a ≤x≤a
-
0
otherwise
a) Determine the normalization constant A
b)
What is the expectation value of x (at time t=0)
c) What is the expectation value of p (at time t=0)
d) Find the expectation value of x²
e) Find the expectation value of p²
f) Find the uncertainty in x (0)
g) Find the uncertainty in p (p)
h) Check that your results are consistent with the uncertainty principle
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