# Study Session 4: Quantum Concepts II

- Page ID
- 31890

**Demonstrate concepts from class**

Show that the eigenfunctions of the 1D particle in a box are orthonormal.

Show that a dipole operator of the form, \(\hat \mu=\mu_0\hat x\) can lead to a transition between two levels in the 1D particle in a box.

Show that eigenfunctions of degenerate energy states of the 2D particle in a box are orthogonal.

How deos a dipole operator of the form \(\hat\mu=\mu_0\hat r=\mu_{0,x}\hat x +\mu_{0,y}\hat y\) affect eigenfunctions of degenerate energy states of the 2D particle in a box? Can it interconvert these states?