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A coherent state of a one-dimensional simple harmonic oscillator is defined to be an eigenstate of the (non-Hermitian) annihilation operator a: a|λ⟩=λ|λ⟩ where λis, in general, a complex number. (a) Prove that |λ⟩=e^-|λ|^2 / 2 e^λ a^†|0⟩ is a normalized coherent state. (b) Prove the minimum uncertainty relation for such a state. (c) Write |λ⟩as |λ⟩=∑n=0^∞ f(n)|n⟩ Show that the distribution of |f(n)|^2 with respect to n is of the Poisson form. Find the most probable value of n, and he
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