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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

E

_{n}= (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?