Propagation of de Broglie waves in 1d - real part of the complex amplitude is blue, imaginary part is green. The probability (shown as the colour opacity) of finding the particle at a given point x is spread out like a waveform, there is no definite position of the particle. As the amplitude increases above zero the curvature decreases, so the amplitude decreases again, and vice versa - the result is an alternating amplitude: a wave. Top: plane wave. Bottom: wave packet.
http://en.wikipedia.org/wiki/Matter_wave
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