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Ground state energy of 5 identical spin 1/2 particle

  • #1
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Homework Statement


The ground state energy of 5 identical spin 1/2 particles which are subject to a one dimensional simple harkonic oscillator potential of frequency ω is
(A) (15/2) ħω
(B) (13/2) ħω
(C) (1/2) ħω
(D) 5ħω

Homework Equations


Energy of a simple harmonic oscillator potential is
En = (n+½) ħω

The Attempt at a Solution


Since the particles have 1/2 spin so they are fermions. So any two particpes cannot be in the same state. So every particle will have a different state and hence a different energy corresponding to that state.
To calculate the ground state so each of the 5 particles will have energy corresponding to n= 0,1,2,3,4

(1/2)ħω
(3/2)ħω
(5/2)ħω
(7/2)ħω
(9/2)ħω

So total energy of the particle is = (25/2)ħω

But this is not the answer. Can you let me what am I doing wrong?
 

Answers and Replies

  • #2
TSny
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So any two particpes cannot be in the same state. So every particle will have a different state and hence a different energy corresponding to that state.
There can be more than one state with the same energy.
 
  • #3
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There can be more than one state with the same energy.
But this is a one dimentional potention. There is no degeneracy.
 
  • #4
TSny
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A possible state of a spin 1/2 particle is to have an energy of ħω/2 with its spin "up". But that's not the only way the particle could have an energy of ħω/2.
 
Last edited:
  • #5
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A possible state of a spin 1/2 particle is to have an energy of ħω/2 with its spin "up". But that's not the only way the particle could have an energy of ħω/2.
Okay. i get it now. Thanks a lot.
 

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