Q1. (5 pts) Consider a particle of mass m in a box with a potential given by $V(x) = \begin{cases} 0, & \text{when } 0 < x < L \\ \infty, & \text{elsewhere} \end{cases}$, if the system is perturbed by $H' = \epsilon \delta(x - \frac{L}{2})$, where $\epsilon$ is a constant. Calculate the first order energy correction for the state of order n. Q2. (8 pts)
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To calculate the first-order energy correction for the state of order n, we need to use perturbation theory. In perturbation theory, we consider the original Hamiltonian H0 and a perturbation term V. Show more…
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