Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Existance of ladder operators for a system

  1. Jul 4, 2012 #1
    I have only heard about the use of ladder operators in connection with the harmonic oscillator and spin states. However, I would expect them to be useful in other systems as well.

    For example, can we find ladder operators for the discrete states of the hydrogen atom, or any other system with discrete energy levels? Are there established conditions that guarantee their existance?

    Thanks for any help.
     
  2. jcsd
  3. Jul 5, 2012 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You also see them as creation and annihilation operators in quantum optics.
    The ladder operator makes sense where there is fixed step-size between states. You can try for a counter example by trying to derive a ladder operator for non-harmonic potentials.
     
  4. Jul 5, 2012 #3

    Bill_K

    User Avatar
    Science Advisor

    They always exist. For any Hamiltonian with eigenstates |n> you can always define an operator, a*|n> = |n+1>. But the question is, can a* be written in a simple form.

    Generally, a simple form will exist for problems with symmetry, for then the operators will yield an algebraic solution. The hydrogen atom is one example of this, see here.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Existance of ladder operators for a system
  1. Ladder Operators (Replies: 11)

  2. Ladder Operator (Replies: 1)

  3. Ladder operators (Replies: 6)

Loading...