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Free Particles and Plane Waves
In quantum mechanics, a free particle is defined as any particle (such as an electron) that does not feel any fore. Since the particle does not feel any force, the energy of that particle remains constant and we can arbitrarily assign a potential energy of zero to any free particle. In such a case, the wave function that describes the free particle is given by a sinusoidal wave and this is referred to as the plane wave. For any free particle, if the momentum of that particle is known precisely, then by the uncertainty principle we have no way of knowing the position of that particle and so the uncertainty in position is infinitely large. This uncertainty in position is exhibited by the fact that the plane wave extends to positive and negative infinity in both directions along the x axis.
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