Forest ModernPhysics

Matter Waves (Wave Particle Duality)

Special relativity said that

[math]E = pc[/math] if m=0

Plank said he could fit the Black Body radiation data assuming that that

[math]E= hf[/math] where [math]h = 6.63 \times 10^{-34} \mbox{ J} \cdot \mbox{s}[/math] = Plank's constant

Combining the two we have

[math] p=\frac{E}{c} = \frac{ h f}{c}[/math]

[math]\Rightarrow[/math] photons have momentum like a particle (mv)

Do particles reciprocate and behave like photons?

De Broglie's Hypothesis

If photons can behave like particles by having momentum

Then can a particle behave like a wave by having wavelength

[math] p=\frac{ h f}{c} = \frac{h}{\lambda}[/math]

or

[math]\lambda_{particle} = \frac{h}{p}[/math]= de Broglie Hypothesis

Davisson and Germer

From hyperphysics: