Statistical physics: Microcanonical distribution and oscillators

[Marcustryi]

Homework Statement

An ideal gas, consisting of N harmonic oscillators of mass m and frequency w and charge q, is placed in an external uniform electric field with intensity e. Find the phase volume limited by the energy hypersurface H(x, p; e)=E. Find an expression for the temperature of the oscillator system.

Relevant Equations

H(x, p; e)=E

Hamilton's function in this case is the sum of potential and kinetic energy? But then I don’t remember or don’t understand what to do with e.
I need to find Г, but I don't understand what to do with the field.

 

[Marcustryi]

H(x,p;e)=sum(for i=1 to N)(p^2/2m+(mw^2)*x^2/2+qex)=E
Гn=(Г1)^N.
But how to calculate the phase volume? what replacement should I make?