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Unformatted text preview: E x ( z ) is ˆ E x ( z ) = E sin( kz ) ± a + a † ² where E is a normalization constant, and a is the photon annihilation operator. We also deﬁne the photon number operator ˆ n by ˆ n = a † a. (a) Let the state of cavity ﬁeld at time t = 0 be  Ψ(0) i =  m i , where m is an integer. Determine  Ψ( t ) i . Then compute the average values of ˆ E x and ˆ n at time t , along with their variances σ E x ( t ) and σ n ( t ) as deﬁned in Section 3.5.1. (b) As above, but for  Ψ(0) i = (  m i + e iϕ  m + 1 i ) / √ 2, where m is a positive integer, and ϕ is a phase. 1 (c) Use (3.62) to establish an uncertainty relation between the electric ﬁeld and the photon number. Verify that your answers above are consistent with this uncertainty relation. 2...
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This note was uploaded on 02/15/2011 for the course PHYS 143B taught by Professor Unknow during the Spring '10 term at Harvard.
 Spring '10
 Unknow
 Physics, mechanics

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