Question

A particle of mass $m$ is in a 1D infinite square well potential centered at $x = 0$ $V(x) = egin{cases} 0 & -frac{a}{2} < x < frac{a}{2} \ infty & ext{otherwise} end{cases}$ (1) [10 points] Find the eigenenergies {$E_n$} and eigenfunctions {$psi_n(x)$ } of the particle. (2) [10 points] Find the uncertainty of the particle's momentum in the eigenstate $|psi_n angle$. (3) [10 points] Assume the initial state of the particle is given by $|psi(0) angle = frac{1}{sqrt{2}}(|psi_1 angle + i|psi_2 angle)$. Find the expectation value of the particle's position at time $t$.

          A particle of mass $m$ is in a 1D infinite square well potential centered at $x = 0$

$V(x) = egin{cases} 0 & -frac{a}{2} < x < frac{a}{2} \ infty & 	ext{otherwise} end{cases}$

(1) [10 points] Find the eigenenergies {$E_n$} and eigenfunctions {$psi_n(x)$ } of the particle.
(2) [10 points] Find the uncertainty of the particle's momentum in the eigenstate $|psi_n
angle$.
(3) [10 points] Assume the initial state of the particle is given by $|psi(0)
angle = frac{1}{sqrt{2}}(|psi_1
angle + i|psi_2
angle)$. Find the expectation value of the particle's position at time $t$.

$A particle of mass m is in a 1D infinite square well potential centered at x = 0 V(x) = egincases 0 -fraca2 < x < fraca2 infty extotherwise endcases (1) [10 points] Find the eigenenergies En and eigenfunctions psin(x) of the particle. (2) [10 points] Find the uncertainty of the particle's momentum in the eigenstate |psin angle. (3) [10 points] Assume the initial state of the particle is given by |psi(0) angle = frac1sqrt2(|psi1 angle + i|psi2 angle). Find the expectation value of the particle's position at time t.$

Added by Rocio R.

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