05_03_28

# 05_03_28 - time t and then measure the position of the...

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[email protected] 108 03/28/2005 Physical correspondence to polarization states y x A y A x + = Ψ With probability * n n n A A P = = Φ = N n n n A x x f 0 ) ( ) ( Polarization states States of the wave function 2 * Ψ = = x A A P x x x x ) ( x n Φ With probability Analyzers: can separate the components of the different basis states x Momentum analyzer Energy levels Measurement: changes the state of the quantum particle. 1 0 2 = = N n n A

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[email protected] 109 03/28/2005 8) The time dependence of quantum states Probability to find a quantum particle in the interval [x,x+dx]: Time dependence of the wave function: The time dependent probability distribution: There is an interference between the wave functions to different energies E. Measuring the time dependent probability distribution requires preparing many equivalent states, letting them evolve for a fixed
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Unformatted text preview: time t and then measure the position of the quantum particle for example by a photographic plate. After a large number of particles have been measure, the image corresponds to the probability distribution at time t. The time averaged probability distribution: If the position is measured at random times after the preparation of the equivalent states, the interferences between different eigenstates of the Schr ö dinger equation wash out . dx t x 2 | ) , ( | Ψ ∑ ∞ =-Φ = Ψ ) ( ) , ( n t i n n n E e x A t x ∑ ∞ = =-Φ Φ = Ψ * * 2 | ) , ( | m n t i m n m n m E n E e A A t x ∑ ∞ = Φ = Ψ 2 2 2 | ) ( | | | | ) , ( | n n n t x A t x...
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## This note was uploaded on 09/28/2008 for the course PHYS 316 taught by Professor Hoffstaetter during the Spring '05 term at Cornell.

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05_03_28 - time t and then measure the position of the...

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