The coherent states la) of a quantum harmonic oscillator are states that minimizesthe uncertainty product, i.e. oop = h/2. These states are eigenfunctions of thelowering operator â, that isâ|a) = ala),where the eigenvalue a can be a complex number.(a) Determine (x), and (x²) in the state la)(b) Determine (p), and (p²) in the state la)(c) Show that 0,0p = ħ/2The coherent state la) can be expressed asla)=1Σenn=0where [n)'s are the harmonic oscillator eigenstates.(d) Show thatCn =(e) By normalizing a, determine co.anCo.

It is said that,The coherent states of a quantum harmonic oscillator are states that minimizes the…

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