(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There are identical particles in a harmonic potential [tex]V(x)=\frac{1}{2}m\omega^{2}x^{2}[/tex]. The number of particles is 2N, where N is a positive integer.

2. Relevant equations

a) What is the system's Hamilton's operator for bosons in the second quantization? How about the fermions?

b) What is the energy of the ground level, if the particles are i) S = 0 bosons, ii) S = 1/2 fermions?

c) Write the state vector of the ground level for S = 0 bosons and S = 1/2 fermions using creation and annihilation operators to vacuum.

3. The attempt at a solution

a) I have no idea...

b) Maybe I have to solve the SchrÃ¶dinger's Equation, and using boudary conditions (?) solve the equation for energy E. There are 2N bosons all in the ground state, because Pauli's Exclusion Principle does not hold for bosons. So, I just put n = 1 to the E-equation and multiply it by 2N. Right? :uhh:

How about fermions? The Pauli Exclusion Principle holds for them, at least...

c) I have no idea...

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Identical particles

**Physics Forums | Science Articles, Homework Help, Discussion**