Question

Density of states for a one-dimensional Fermi system is proportional to:

• A. \( E \)
• B. \( E^{1/2} \)
• C. \( E^{-1/2} \)
• D. A constant

Hint:

The density of states decreases as \( E^{-1/2} \) in a one-dimensional system.

Answer 1

The Correct Option is C

The density of states \( g(E) \) in a system is given by:
\[ g(E) \propto \frac{dN}{dE} \] For a 1D Fermi gas, the density of states follows:
\[ g(E) \propto E^{-1/2} \]