A matter wave is when you think of matter as a wave. The concept of matter waves was first introduced by Louis de Broglie. It's a hypothetical wave associated with the motion of a particle of atomic or subatomic size that describes effects such as the diffraction of beams of particles by crystals.
This graphic shows two voltage-time graphs for two sine waves in phase and out of phase. Phase refers to the relationship of two waves (signals) to each other. If both signals are at their highest peak (+) at the same time they are in phase, otherwise they are out of phase with each other. For example, if one signal is at its highest peak (+) while the other signal is at its lowest peak (-) they are 180 degrees out of phase. On our diagram the waves are 90 degrees out of phase.
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