237module7 - Quantum Mechanics I Module 7 Getting Started 1...

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

View Full Document Right Arrow Icon
Quantum Mechanics I - Module 7 Getting Started 1. What are the raising and lowering operators? 2. Why are the raising and lowering operators important in quantum me- chanics? Enrichment Problem Consider the harmonic oscillator (with = m = ω = 1) given by: H = p 2 2 + x 2 2 . Define: a = 1 2 ( p - ix ) a = 1 2 ( p + ix ) 1. Show that [ a, a ] = 1 . 2. Show that H = a a + 1 2 . 3. Show that [ a a, H ] = 0 . 4. Show that if | n is an eigenstate of N = a a with eigenvalue
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