PHYS411_HW5 v2.pdf

# PHYS411_HW5 v2.pdf - Physics 411 HW#5 Due at the start of...

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Physics 411 HW#5 Due at the start of class Friday, Nov 11th Reading: Please read Griffiths 3.4-3.5 this week. You can skip 3.5.3 Office Hours: Mondays, 4:00-5:30 PM in DRL 4E6 Problem 1 In our proof of the Generalized Uncertainty Relation in class, σ A σ B ≥ | 1 2 h [ ˆ A, ˆ B ] i| , we found that the minimum uncertainty could only be achieved when Δ ˆ A | ψ i = λ Δ ˆ B | ψ i and h Δ ˆ A Δ ˆ B + Δ ˆ B Δ ˆ A i = 0, where Δ ˆ A ˆ A -h ˆ A i . We have claimed that the Gaussian wavefunction ψ ( x ) = Ae - ax 2 satisfies the minimum uncertainty relation for the operators ˆ x and ˆ p . (a) Prove that Δˆ x | ψ i = λ Δˆ p | ψ i for the Gaussian wavefunction given above. (b) Prove that h Δˆ x Δˆ p + Δˆ p Δˆ x i = 0 for the Gaussian wavefunction given above. Now define a new wavefunction
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