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
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
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?