# Quantum
## A3 Particle in mathematical box
Consider a potential of the form:
$V(x) = \begin{cases} 0 & x \in [e, \pi] \\ \infty^{\infty} & \end{cases}$
Write down the term for the Energy levels and for the wavefunction
## A4 Particle in a double box
Consider a potential of the form:
$V(x) = \begin{cases} 0 & x \in [0,l] \text{ or } x\in [2l, 2l+L] \\ \infty \end{cases}$
**a)** Solve the schrödinger Equation for both boxes separateley (box of length $l$ and box of lenght $L$)
**b)** Why and how can both solutions be superimposed?
**c)** Can the particle tunnel from one box to the next?
**d)** How would you determine in which box the particle resides in?