Tuesday, October 11, 2011

Wave-particle duality from Quantum Mechanics

Wave-Particle Duality is the ptindiples that light and matter exhibit the properties of both waves and particles. This is a key concept of quantum mechanics shows that subatomic particles have a dual nature that is some times they act like particles, exhibiting properties like scattering and at other times they behave as waves, exhibiting properties like interference and diffraction.

The photoelectric effect is the case where photons of light eject electrons from a sheet of metal like interacting partials are supposed to behave. The Davission-Germer experiment has an electron beam is aimed a nickel crystal in whith the resulting scattering has peeks and valise do to diffraction.

The wave length of a particle's wave is l = h / p.  Where l is the wave length, p is momentum  h is Planck's constant  Now this relationship is just the first part of wave particle duality. The actual wave function is denoted by Y (Psi).  While the exact formula varies with the situation, the wave function is always a complex number. It is related to the probability of finding the particle at a given point in pace.

The probability of finding a partial at a given point in space is denoted by |Y(x)|2 also denoted by Y* Y  where the complex number is  Y = A + iB and the complex conjugate: Y* = A – iB The over all space the probability density = 1.

In conclusion matter behaves as both particles and waves. The wave nature is related to the probability of finding a particle at a given location at a given time.

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