Matter Wave Visualization

All matter has wave-like properties: every moving particle has a de Broglie wave λ = h/p.

Quantum mechanics replaces the classical concept of trajectory with the wave function ψ(x,t) — |ψ|² is the probability density.

Bound states (atoms, nuclei) are described by standing matter waves — explains discrete energy levels.

Matter waves can interfere and diffract like light. Experimental demos: electron diffraction (Davisson-Germer), neutron interferometry, atom interferometers.

Matter waves do NOT travel at v_particle in general — phase velocity v_p = E/p, group velocity v_g = dE/dp = v_particle.

For a relativistic particle: v_p · v_g = c² (so v_p > c for massive particles — but this carries no information).

Macroscopic objects have λ_dB so small that wave behaviour is hidden — but it is THERE, in principle.