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The coherent states for the one-dimensional harmonic oscillator are defined as eigenstates of the operator
of annihilation a (which is non-Hermitian):
a |λ⟩ = λ |λ⟩ (1)
where λ is a complex number in general.
a)prove that is a normalized consistent state.
b)Show that the above state satisfies the minimum uncertainty relation, i.e., show that
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