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lecture10 - 5.61 Fall 2007 Lecture#10 page 1 THE POSTULATES...

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Unformatted text preview: 5.61 Fall 2007 Lecture #10 page 1 THE POSTULATES OF QUANTUM MECHANICS (time-independent) Postulate 1: The state of a system is completely described by a wavefunction ψ ( r , t ) . Postulate 2: All measurable quantities (observables) are described by Hermitian linear operators. Postulate 3: The only values that are obtained in a measurement of an observable “A” are the eigenvalues “ a n ” of the corresponding operator “ A ˆ ”. The measurement changes the state of the system to the eigenfunction of A ˆ with eigenvalue a n . Postulate 4: If a system is described by a normalized wavefunction ψ , then the average value of an observable corresponding to A ˆ is a = ∫ ψ * A ˆ ψ d τ Implications and elaborations on Postulates 2 #1] (a) The physically relevant quantity is ψ ψ * ( r , t ) ψ ( r , t ) = ψ ( r , t ) 2 ≡ probability density at time t and position r (b) ψ ( r , t ) must be normalized ∫ ψ * ψ d τ = 1 (c) ψ ( r , t ) must be well behaved 5.61 Fall 2007 Lecture #10 page 2 (i) Single valued (ii) ψ and ψ ′ continuous (iii) Finite #2] (a) Example: Particle in a box eigenfunctions of...
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This note was uploaded on 09/24/2011 for the course MATH 1090 taught by Professor Greenwood during the Spring '08 term at MIT.

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lecture10 - 5.61 Fall 2007 Lecture#10 page 1 THE POSTULATES...

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