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Quantum Theory

  The theory of quantum mechanics is one of the great achievements of 20th-century physics. It has been rigorously tested and shown to be valid in a huge variety of situations. Modern computers and electronics are designed using quantum mechanics.

Quantum mechanics involves mathematics, and cannot properly be understood without it. Central to the theory are the concepts of wave functions and operators. The motion of a quantum mechanical particle is described by a wave function Ψ, which is analogous to the amplitude describing the motion of a wave, providing we accept the wave nature of matter and transfer from a wave to a particle concept. The probability of finding the particle in a certain place is given by Ψ2.

All properties of a particle have corresponding mathematical operators. These can be simple or complex the operators for momentum and position are d/dx and x respectively. The operators and wave functions are combined to give matrix elements, which correspond to observable properties of the particles. Thus, to find an equation describing a property of a particle, we first find its wave function (not usually a simple process!) and then use the operator corresponding to the property of interest in to produce the matrix element which we may observe.

An important part of quantum theory is the uncertainty principle. This is a natural consequence of the wave nature of matter, and means that it is impossible to measure both the position and the momentum of a particle at the same time with perfect accuracy. JJ

See also quantization; Schrödinger equation; wave-particle duality.



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