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phy-4600/Postulates
2016-02-12 12:26:39 -05:00

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(1) A general state vector is represented by |Ψ> (a ket)
(2) A physical observable is represented by an operator A that acts on |Ψ>
(3) The possible measurements of an observable are the eigenvalues aₙ of the operator A
(4) The probability of measuring eigenvalue aₙ is given by Paₙ=|<aₙ|Ψ>|²
(5) After a measurement A that yields aₙ, the quantum system is in a new state that is the normalized projection of the original system ket onto the ket (or kets) corresponding to the result of the measurement:
|Ψ'> = Pn|Ψ> / √(<Ψ|Pn|Ψ>)
(6) The time-evolution of the quantum system is determined by the Hamiltonian operator H(t) through the Schrodinger equation
ιħ(d/dt)|Ψ(t)> = H(t)|Ψ(t)>