Unformatted text preview: α = 0, the coherent state  α =0 A is exactly equal to the harmonic oscillator groundstate,  n =0 A . Then show that any other coherent state can be created by acting on the groundstate,  A , with the ‘displacement operator’ D ( α ), i.e. show that  α A = D ( α )  A , where D ( α ) := e αA † − α * A (1) You may need the Zassenhaus formula e B + C = e B e C e − [ B,C ] / 2 , which is valid only when [ B, [ B,C ]] = [ C, [ B,C ]] = 0. What is D ( α 2 )  α 1 A ? 3. [15 pts] Consider a system described by the Hamiltonian H = p κ ( A + A † ). Use your results from the previous problem to determine  ψ ( t ) A for a system initially in the groundstate,  ψ (0) A =  A . 4. [10pts each] Cohen Tannoudji, pp341350: problems 3.6, 3.7, 3.11 1...
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 Fall '09
 M.Moore
 mechanics, Work, coherent, coherent state, parity operator, harmonic oscillator groundstate

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