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notes06-07-page34 - ψ represents a probability amplitude...

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2. The Postulates of Quantum Mechanics 2.1. Postulate I Postulate I : The state of a system is de fi ned by a wavefunction, ψ, which con- tains all the information that can be known about the system. We will normally take ψ to be a complex valued function of time and coordi- nates: ψ ( t, x, y, z ) and, in fact, we will most often deal with time independent “stationary” states ψ ( x, y, z ) Note: In general the wavefunction need not be expressed as a function of coordi- nate. It may, for example, be a function of momentum.
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Unformatted text preview: ψ represents a probability amplitude and is not directly observ-able. However the mod-square of the wavefunction, ψ ∗ ψ = | ψ | 2 , represents a probability distribution which is directly observable. That is, the probability of fi nding a particle which is described by ψ ( x, y, z ) at the position between x and x + dx, y and y + dy and z and z + dz is | ψ ( x, y, z ) | 2 dxdydz (or | ψ ( r, θ, φ ) | 2 r 2 sin θdrdθdφ in spherical coordinates). 22 22...
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