Question

Phase space area of a 1-D SHO with mass \(m\), angular frequency \(\omega\) and having energy between \(E\) and \(2E\) is:

• A. \( \frac{2\pi E}{\omega} \)
• B. \( \frac{4\pi E}{\omega} \)
• C. \( \pi E \)
• D. \( 0 \)

Hint:

Phase space area in classical mechanics is an important quantity in Liouville's theorem.

Answer 1

The Correct Option is B

For a 1-D simple harmonic oscillator, the phase space area is given by:
\[ A = \int_{E}^{2E} dp \, dq \]