Hydrogen-Like atom

incomplete

$$\psi (r,\theta ,\varphi )=R(r)Y_{lm}(\theta ,\varphi )$$

• Any particle with 1 electron is hydrogen-like. Neutrons and Protons don’t really matter. Multi particle systems not covered until grad level. Potential for HLS given by

$$V(r)=-\frac{z{e}^2}{4\pi {ϵ}_{0}r};z=1$$

Solution for R

$$R(r)=r^{l}Fn(r)e^{-\sqrt{2m_{0}E/{\hslash }^2}r}$$

Energy levels given by:

$$E_n=-\frac{(13.6ev)Z^2}{n^2};n=1,2,3,\dots$$

Coulomb Potential shown above. Bound state. N is quantum number for $L_z$ Particle is in bound state because E is less then V. See also 1 dimensional bound state.