01. Physical Background and Wave-Particle Duality

1.1 The Photoelectric Effect: Waves as Particles

Photoelectric Effect

$$E_{\text{kinetic}}=-E_0+\hslash w$$

where

$E_0>0$ is a constant energy (depends on particular metal)
$\hslash$ is the constant of proportionality
$\omega$ is angular velocity

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Einstein-Planck Relation

$$E=\hslash \omega$$

where $E$ is the energy of the light of angular frequency $\omega$ existing in small packets

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1.2 Emission / Absorption Spectra of Atoms: Discreteness

Energies of Hydrogen Atom

$$E_n=-\frac{2\pi R_0\hslash c}{n^2}$$

where $n\in \mathbb{Z}$ and $R_0$ is the Rydberg’s Constant

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1.3 The Double Slit Experiment: Particles as Waves

Not Applicable

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1.4 De Broglie’s Matter-Waves

De Broglie's Relations

Suppose there is a free particle of energy $E$ and momentum $\mathbf{p}$ with wave of angular frequency $\omega$ and wave vector $\mathbf{k}$

de Broglie relations are

$$\begin{array}{rl}E& =\hslash \omega \\ \mathbf{p}& =\hslash \mathbf{k}\end{array}$$

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