Particle in a Box Questions

1. An electron is moving in a 1D box on infinite height and width 1Å. Find the minimum energy of the electron.

2. Solve Schrodinger equation for a particle of mass m in an infinite rectangular well defined by $V(x)=0$ at $\frac{-L}{2} \le x \le \frac{L}{2}$ and $V=\infty$ at $x > \frac{L}{2}$ and $x < \frac{-L}{2}$. Obtain the normalized Eigen functions and corresponding eigen values.

3. A particle trapped in an infinitely deep square well of width $a$ has a wave function $ψ = (\frac{2}{π})^\frac{1}{2} sin \frac{πx}{a}$. The walls are suddenly separated by infinite distance. Find the probability of the particle having momentum between $p$ and $p+dp$. [Mains 2015]