de Broglie Matter Waves

Particle Electron

⚛️Electron

🔵Proton

⚪Neutron

⚽Ball

Kinetic Energy —

slowfast

Coherence Length 50%

localizedspread out

Propagating Matter Wave — Real part of ψ(x,t)

Wavelength λ

—

de Broglie

Momentum p

—

kg·m/s

Phase Velocity

—

v_phase = E/p

Quantum?

Yes

λ > atom size

Loading…

Wavelength Scale — All particles at same speed

Speed (% of c) 0.01%

Quantum Number n — Standing Matter Waves

n = 1

n = 2

n = 3

n = 4

n = 5

n = 6

de Broglie Standing Wave on Circular Orbit

Quantum # n

integer only

Orbit radius

a₀

r = n²·a₀

Wavelengths / orbit

2πr = nλ

Angular Momentum

ℏ

L = nℏ (Bohr)

Bohr's Quantization Explained by de Broglie: An electron can only exist in orbits where its matter wave forms a perfect standing wave — the wave must close on itself: 2πr = nλ. Non-integer n values would cause destructive interference, making those orbits forbidden. This explains why angular momentum is quantized: L = nℏ follows directly from 2πr = nλ combined with λ = h/p.