Problem 1.16 | Griffiths' Introduction to Quantum Mechanics | 3rd Edition
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Problem 1.16
A particle is represented (at time t=0) by the wave function
$\Psi (x,0) = \begin{cases} A(a^2-x^2), -a \le x \le a \\ 0, \text{otherwise} \end{cases}$
(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 $\langle p \rangle =md \langle x \rangle /dt$. Why not?)
(d) Find the expectation value of $x^2$.
(e) Find the expectation value of $p^2$.
(f) Find the uncertainty in x $(\sigma_x)$.
(g) Find the uncertainty in p $(\sigma_p)$.
(h) Check that your results are consistent with the uncertainty principle.
https://tru-physics.org/2023/03/11/pr...
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