Ground state energy of 5 identical spin 1/2 particle

[Sushmita]

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?

 

[TSny]

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.

 

[Sushmita]

There can be more than one state with the same energy.

But this is a one dimensional potention. There is no degeneracy.

 

[TSny]

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.

 

[Sushmita]

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.

 

[Chacha vidhayk hai h]

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?
Here filling of electron will be 2,2,1=5
So E=2(0+1/2)hcutw +2(1+1/2)hcutw+1(2+1/2)hcutw
E= 13/2hcutw