Minimum Energy of Noninteracting Particles in 1D Box: Spin 1/2, 1, 3/2

[aznkid310]

Homework Statement

What is the minimum possible energy for five noninteracting spin 1/2 particles of mass m in a one-dimensional box of length L? What if the particles were spin 1? Spin 3/2?

Homework Equations

Could someone get me started?

The Attempt at a Solution

U = [-e/(m_e)](sqrt[3]/2)(h_bar)B, where h_bar = 1.055E-34
m_e = electron mass
e = electron charge
B = magnetic field

 

[SporadicSmile]

You need the wavefunction for particles in an infinite square well (which is the same as this box). Then feed in your particles to the energy levels, as you would in an atom, then calculate the energy of the last electron in the orbital. Do the same for spin 1 and spin 3/2 particles. Take care with what spin states a level can have, and whetherthe particles are fermions or a bosons.

 

[epenguin]

I think this problem has a conceptual part you are being tested on, not requiring calculation really, and a more mathematical part.
Before starting the math part which maybe is getting in the way, state the concept which will indicate too how you have to proceed for the math part.
In each case will the electrons all have the same energies as each other?

 

[DeShark]

In each case will the electrons all have the same energies as each other?

These aren't electrons! They're non-interacting. This makes the question much easier.

 

[aznkid310]

wave function y = (sqrt(2)/L)*sin[k(pi)x/L]

Do i use the fact that y_s = y(1)y'(2) + y'(1)y(2) because it is symmetric?

Im not sure how to use this

 

[epenguin]

In each case will the electrons all have the same energies as each other?

These aren't electrons! They're non-interacting. This makes the question much easier.

OK.

In each case will the particles all have the same energies as each other?

 

[guro]

I really want to solve this same problem pls help...

 

[guro]

What is the minimum possible energy for five noninteracting spin 1/2 particles of mass m in a one-dimensional box of length L? What if the particles were spin 1? Spin 3/2?