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## Homework Statement

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.

## Homework 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.

## The Attempt at a Solution

a) I have no idea...

b) Maybe I have to solve the Schrödinger'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...

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