Step 1: Recall the concept of matter waves.
According to de Broglie’s hypothesis, moving particles such as electrons exhibit wave-like properties.
Step 2: Identify G. P. Thomson’s contribution.
G. P. Thomson experimentally verified the wave nature of electrons by passing them through thin metal foils.
Step 3: Observe the phenomenon involved.
The electrons produced diffraction patterns, similar to X-ray diffraction, which is a characteristic property of waves.
Step 4: Analyze the options.
(A) Diffraction — direct evidence of wave nature ✔
(B) Refraction — not observed for electrons
(C) Polarization — applies to transverse waves like light
(D) Scattering — not specific proof of wave nature
Step 5: Final conclusion.
The phenomenon that confirmed the existence of matter waves is diffraction.
\[
\boxed{\text{(A)}}
\]