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!

N spin 1/2 particles in 3D harmonic oscillator potential

  1. Dec 16, 2012 #1
    1. The problem statement, all variables and given/known data
    The 3-dimensional harmonic oscillator potential holds N identical non-reacting spin 1/2 particles

    a)How many particles are needed to fill the low lying states through E=(3+3/2)[itex]\bar{h}[/itex]ω

    b)What is the total energy of the system

    c)what is the fermi energy


    2. Relevant equations
    E=(n+3/2)[itex]\bar{h}[/itex]ω
    n=nx+ny+nz=3


    3. The attempt at a solution
    a)(1,0,0)*3,(1,1,0)*3,(2,0,0)*3,(1,1,1),(2,1,0)*6,(3,0,0)*3
    19 states for 38 total particles
    b)6E1+12E2+20E3=147[itex]\bar{h}[/itex]ω
    c)Ef=(3+3/2)[itex]\bar{h}[/itex]ω
    -------------------------------------------------------------------
    So I'm pretty sure I did part a correct. If so part b should just be the sum of the number of particles at each energy right?

    For part c isn't the given energy the fermi energy since I'm finding all the states below it?

    I'm not really sure about my reasoning on the part b and c
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?