If $\psi_n(\mathbf{r})$ is the normalized eigenfunction of the time-independent Schrodinger equation, corresponding to energy eigenvalue $E_n$, show that $\left|\psi_n(\mathbf{r})\right|^2$ is not only the probability density for the coordinate vector $\mathbf{r}$, if the system has energy $E_n$, but also conversely the probability of finding the energy to be $E_n$, if the system is known to be at position $\mathbf{r}$.