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Unformatted text preview: Lecture 15, p.1 Lecture 15: TimeDependent QM & Tunneling Review and Examples, Ammonia Maser 0 L U x U(x) E x  ψ (x,t ) 2 U= ∞ U= ∞ x L  ψ (x,t=0) 2 U= ∞ U= ∞ x L Lecture 13, 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 . 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 π Ψ = = +  Ψ (x,t) 2 U= ∞ U= ∞ x L  Ψ (x,0) 2 U= ∞ U= ∞ x L Lecture 15, p.4 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:...
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This note was uploaded on 02/21/2011 for the course PHYS 214 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Staff
 Energy

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