## Photon energy

$E_{Photon} = \frac{hc}{\lambda} = hf = \hbar\omega$

## Photoelectric effect

$hf = W_{Out} + K = W_{Out} + eU_0$

## DeBroglie wavelength

$\lambda = \frac{h}{p} = \frac{h}{mv}$

## Square well potential

$E_n = \left(\frac{h^2}{8mL^2}\right) \cdot n^2$
$\Psi_n(x) = \sqrt{\frac{2}{L}} \sin \left( n\frac{\pi x}{L} \right)$

$r = \frac{\epsilon_0h^2}{\pi \mu e^2}\frac{n^2}{Z}\approx a_0 \cdot \frac{n^2}{Z}$
$a_0=0.529 \; \textup{Å}$

## Rydberg's formula

$\frac{1}{\lambda} = R_M \cdot Z^2 \left( \frac{1}{n^2_1} - \frac{1}{n^2_2} \right)$
$R_M = \frac{e^4}{8 \varepsilon^2_0 h^3 c}\cdot \mu$
$\mu = \frac{m \cdot M}{m + M} \; \textup{Reduced mass}$
$R_M = R_\infty \cdot \frac{M}{M+m}$
$R_{\infty} = 109737.31568 \; \textup{cm}^{-1}$

## Energy levels in Hydrogen

$E_n = -Z^2 \frac{E_0}{n^2} \;\; \textup{where} \;\; E_0 = \frac{mk^2 e^4}{2 \hbar^2} = 13.6 \; \textup{eV}$

## Quantized angular momentum z component

$L = \hbar \sqrt{l(l+1)}$

## Quantized angular momentum

$|L| = \hbar\sqrt{l(l+1)}$

## Ratio between the proton mass and the electron mass

$\frac{m_p}{m_e} = 1836.152 673$

## Characteristic X-ray emission

$\frac{1}{\lambda_{K_{\alpha}}} = \frac{3}{4}R_{\infty} \cdot (Z-1)^2$
$\frac{1}{\lambda_{L_{\alpha}}} = \frac{5}{36}R_{\infty} \cdot (Z-7.4)^2$

## Bremsstrahlung

$\lambda_{min} = \frac{hc}{eU}$

## Reduced mass

$\mu = \frac{m_1 m_2}{m_1 + m_2}$

## Moment of inertia

$I=\mu r^2$

## Angular momentum

$L = \mu r v = \mu r^2 \omega = I\omega$

## Rotational energy diatomic molecule

$E_{rot} = \frac{l(l+1)\hbar^2}{2I}, \; I=\mu r^2$

## Rotational constant

$B = E_{0 r} = \frac{\hbar^2 }{2 I}$

## Vibrational energy diatomic molecule

$E_{vib} = \hbar \omega_0 \cdot (\nu + 1/2)$

## Fermi energy at T=0 K

$E_F = \frac{h^2}{8m}\left( \frac{3}{\pi}n\right)^{2/3}, \textup{where n is the electron density}$

## Fermi temperature

$T_F = \frac{E_F}{k}$

## Fermi speed

$u_F = \sqrt{\frac{2 E_F}{m_e}}$

## Free electrons in conductors

$n_e = f \cdot \frac{\rho \cdot N_A}{M}, \textup{where f is the number of free electrons per atom}$

## Resestivity

$\rho = \frac{m_e v_{av}}{n_e e^2 \lambda}$

## Mean free path

$\lambda = \frac{v t}{n_{ion} \pi r^2 v t} = \frac{1}{n_{ion} \pi r^2} = \frac{1}{n_{ion} A}$

## Specific heat due to conduction electrons

$c_v = \frac{1}{2} \pi^2 \cdot R \cdot \frac{T}{T_F}$