The coherent states la) of a quantum harmonic oscillator are states that minimizes the uncertainty product, i.e. oop = 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 (x), and (x²) in the state la) (b) Determine (p), and (p²) in the state la) (c) Show that 0,0p = ħ/2
The coherent states la) of a quantum harmonic oscillator are states that minimizes the uncertainty product, i.e. oop = 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 (x), and (x²) in the state la) (b) Determine (p), and (p²) in the state la) (c) Show that 0,0p = ħ/2
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Transcribed Image Text:The coherent states la) of a quantum harmonic oscillator are states that minimizes
the uncertainty product, i.e. oop = 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 (x), and (x²) in the state la)
(b) Determine (p), and (p²) in the state la)
(c) Show that 0,0p = ħ/2
The coherent state la) can be expressed as
la)=1
Σen
n=0
where [n)'s are the harmonic oscillator eigenstates.
(d) Show that
Cn =
(e) By normalizing a, determine co.
an
Co.
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