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

Question on quantum numbers

  1. Feb 11, 2015 #1
    I don't understand why quantum numbers can not be divided into half integers and so on. The books I have read do not give clear explanations. Would anyone mind helping me understand this? Thanks!
     
  2. jcsd
  3. Feb 11, 2015 #2

    bhobba

    Staff: Mentor

    What quantum numbers are you talking about?

    If you are talking about spin quantum numbers then any decent book on QM will prove from the angular momentum commutation relations why its quantized.

    If you are talking about solutions to Schroedinger's equation then that is not always quantized, and when it is it depends entirely on the Hamiltonian:
    http://www.physics.ox.ac.uk/Users/smithb/website/coursenotes/qi/QILectureNotes3.pdf

    Thanks
    Bill
     
  4. Feb 11, 2015 #3
    That was really helpful! Thanks a lot! :)
     
  5. Feb 12, 2015 #4

    stevendaryl

    User Avatar
    Staff Emeritus
    Science Advisor

    The Schrodinger equation: [itex]H \psi = E \psi[/itex] can be solved for arbitrary values of [itex]E[/itex], but when [itex]E[/itex] is not an eigenvalue of the hamiltonian, then [itex]\psi[/itex] will be unnormalizable--it will blow up at infinity, or at the origin, or somewhere. For example, a solution to the free particle Schrodinger equation with [itex]E < 0[/itex] is: [itex]\psi = e^{\hbar K x}[/itex], which corresponds to an energy of [itex]-\hbar^2 K^2/(2 m)[/itex].

    The differential equations for the wave function are forced to have discrete values by boundary conditions: to make sure that the wave function is single-valued in the whole domain, and to make sure that the integral of [itex]|\psi|^2[/itex] is finite.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Question on quantum numbers
  1. Quantum Numbers (Replies: 3)

Loading...