Question

The wavefunction of a particle in an infinite one-dimensional potential well at time $t$ is
$\Psi(x, t) = \sqrt{\frac{2}{3}} e^{-iE_1 t/\hbar}\psi_1(x) + \frac{1}{\sqrt{6}} e^{i\pi/6} e^{-iE_2 t/\hbar} \psi_2(x) + \frac{1}{\sqrt{6}} e^{i\pi/4} e^{-iE_3 t/\hbar} \psi_3(x)$where $\psi_1$, $\psi_2$, and $\psi_3$ are the normalized ground state, the normalized first excited state, and the normalized second excited state, respectively. $E_1$, $E_2$, and $E_3$ are the eigen-energies corresponding to $\psi_1$, $\psi_2$, and $\psi_3$, respectively. The expectation value of energy of the particle in state $\Psi(x,t)$ is

• A. $\frac{17}{6} E_1$
• B. $\frac{2}{3} E_1$
• C. $3 E_1$
• D. (14 E_1)

Answer 1

Answer: (A)

$\frac{17}{6} E_1$

Answer 2

The correct option is (A) :$\frac{17}{6} E_1$