Lect15 - Lecture 15: Time-Dependent QM & Tunneling...

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Lecture 15, p.1 Lecture 15: Review and Examples, Ammonia Maser 0 L U 0 x U(x) E x | ψ (x,t 0 )| 2 U= U= 0 x L | ψ (x,t=0)| 2 U= U= 0 x L
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Lecture 15, p 2 Measurements of Energy What happens when we measure the energy of a particle whose wave function is a superposition of more than one energy state? If the wave function is in an energy eigenstate (E 1 , say), then we know with certainty that we will obtain E 1 (unless the apparatus is broken) . If the wave function is a superposition ( ψ = a ψ 1 +b ψ 2 ) of energies E 1 and E 2 , then we aren’t certain what the result will be. However: We know with certainty that we will only obtain E 1 or E 2 !! To be specific, we will never obtain (E 1 +E 2 )/2 , or any other value. What about a and b? |a| 2 and |b| 2 are the probabilities of obtaining E 1 and E 2 , respectively. That’s why we normalize the wave function to make |a| 2 + |b| 2 =1 .
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Lecture 15, p.3 Example An electron in an infinite square well of width L = 0.5 nm is (at t=0) described by the following wave function: Determine the time it takes for the particle to move to the right side of the well. 2 2 ( , 0) sin sin x t A x x L L L π Ψ = = + | Ψ (x,t)| 2 U= U= 0 x L | Ψ (x,0)| 2 U= U= 0 x L
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Lecture 15, p.4
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Lecture 15, p.5 ACT 1 An electron in an infinite square well of width L = 0.5 nm is (at t=0) described by the following wave function: 2 2 ( , 0) sin sin x t A x x L L L π Ψ = = + 1 ) Suppose we measure the energy. What results might we obtain?
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This note was uploaded on 01/19/2012 for the course PHYS 214 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.

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Lect15 - Lecture 15: Time-Dependent QM & Tunneling...

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