- #1
skrat
- 748
- 8
Homework Statement
An electron in hydrogen atom can be described with normalized wavefunction ##\psi (r,\vartheta ,\varphi )=(\frac{1}{64\pi r_B^3})^{\frac{1}{2}}exp(-\frac{r}{4r_B})##.
Calculate the probability that the electron is in ground state of hydrogen atom. How much is the energy of electron in state ##\psi ##?
Ground state is ##\psi (r,\vartheta ,\varphi )=\frac{1}{\sqrt{4\pi }}\frac{2}{r_B^{3/2}}exp(-\frac{r}{r_B})##
Homework Equations
The Attempt at a Solution
I have no idea on how to even start with the fist part - calculating the probability...
But the second part should be relatively easy to do: ##\left \langle \psi\left | \hat{H} \right | \psi \right \rangle=\left \langle \psi\left | \frac{\hbar^2}{2m}\hat{p}^2+\frac{\hat{l}^2}{2m\left \langle r \right \rangle^2}-\frac{e^2}{4\pi \varepsilon _0}\frac{1}{\hat{r}} \right | \psi \right \rangle##
But still... what is the idea behind the first question?