**Unformatted text preview: **α = 0, the coherent state | α =0 A is exactly equal to the harmonic oscillator ground-state, | n =0 A . Then show that any other coherent state can be created by acting on the ground-state, | 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 ground-state, | ψ (0) A = | A . 4. [10pts each] Cohen Tannoudji, pp341-350: 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 ground-state