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

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern