1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

L, m quantum numbers of 3D oscillator

  1. May 28, 2016 #1
    1. The problem statement, all variables and given/known data
    6 degenerate energy states at E=7/2 h-bar w in isotropic 3D harmonic oscillator.
    pick one possible state( for example, (nx,ny,nz)=(1,0,1)), and find possible l, m quantum numbers
    you may use orthonormality of spherical harmonics


    2. Relevant equations
    pick one possible state( for example, (nx,ny,nz)=(1,0,1)), and find possible l, m quantum numbers


    3. The attempt at a solution
    I tried to understand why the question said 'you may pick (1,0,1), and got it.
    But I have no idea with orthonormality. What I know about it is just

    double integral 0 to pi and 0 to 2pi (Y(l,m), Y(l',m'))sin(theta)d(theta)d(phi) = delta(mm')delta(ll')

    sorry for bad notations.

    How can I use this property to get quantum number l, m at (nx, ny, nz)=(1,0,1) ?

    also, how can I change quantum numbers from carte to polar and from polar to carte
     

    Attached Files:

  2. jcsd
  3. May 28, 2016 #2

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    Do you know the functional form of the eigenstate corresponding to (nx,ny,nz)=(1,0,1) in Cartesian coordinate?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: L, m quantum numbers of 3D oscillator
Loading...