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1. Bosonic Coherent States Let z E C and let 7 be the Fock space of a single bosonic mode a, satisfying the usual algebra [a, a¹] = 1. Consider then the state |(2, 2)) = exp(atz – za)|0), - (2) where [0) is the vacuum state. The state (z, z)) is known as a bosonic coherent state. 1.1. Show that, (1) |¥(2, 2)) = exp ( − 1|2|²) exp(za¹)[0). (3) The vector |z) = exp(za¹)[0) is known as a holomorphic representative of the coherent state (2, 2)).