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y normalizing a, determine co.

y normalizing a, determine co.

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pls answer d and e

The coherent states a) of a quantum harmonic oscillator are states that minimizes the uncertainty product, i.e. ₂0p = h/2. These states are eigenfunctions of the lowering operator â, that is â|a) = ala), where the eigenvalue a can be a complex number. (a) Determine (r), and (²) in the state la) (4 pts). (b) Determine (p), and (p²) in the state la) (4 pts). (c) Show that σ₂0p = ħ/2 (2 pts). The coherent state la) can be expressed as |a) = [cn |n), n=0 where [n)'s are the harmonic oscillator eigenstates. (d) Show that (3 pts) Cn = (e) By normalizing a, determine co. (2 pts) Co.
Transcribed Image Text:The coherent states a) of a quantum harmonic oscillator are states that minimizes the uncertainty product, i.e. ₂0p = h/2. These states are eigenfunctions of the lowering operator â, that is â|a) = ala), where the eigenvalue a can be a complex number. (a) Determine (r), and (²) in the state la) (4 pts). (b) Determine (p), and (p²) in the state la) (4 pts). (c) Show that σ₂0p = ħ/2 (2 pts). The coherent state la) can be expressed as |a) = [cn |n), n=0 where [n)'s are the harmonic oscillator eigenstates. (d) Show that (3 pts) Cn = (e) By normalizing a, determine co. (2 pts) Co.
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