# System of identical particles

1. Aug 13, 2009

### Petar Mali

$$\sum^{3N}_{i=1}\frac{p^2_i}{2m}\leq E$$

Why I can write this inequality? Is this $$E$$ energy of system?

2. Aug 13, 2009

### Petar Mali

For system of $$N$$ identical linear harmonic oscilators of mass $$m$$, frequency $$\omega$$ find phase volume, entropy and energy per particle.

$$H(p,x)=\sum^{N}_{i=1}\frac{p^2_i}{2m}+\frac{1}{2}\sum^{N}_{i=1}m\omega^2x^2\leq E$$

Why inequality? Can I get some explanation?

Thanks!

3. Aug 13, 2009

### clem

The second sum can't be negative.

4. Aug 13, 2009

### Feldoh

I don't really know too much but...

$$\sum^{3N}_{i=1}\frac{p^2_i}{2m}\leq E$$

Looks like it's saying that the sum of the kinetic energy is less than or equal to the total energy, which makes sense to me.