Question

Problem 3 (25 points) 2-dimensional density of states for a gas of particles: Assume there is a gas of particles confined to a two-dimensional region of space which we can consider to be a square in which each side has length $L$. The wavefunction and energy levels for the infinite two-dimensional square well can be written as $\psi(x,y) = A \sin(\frac{n_x \pi x}{L}) \sin(\frac{n_y \pi y}{L})$ $E = \frac{\hbar^2 \pi^2}{2mL^2} (n_x^2 + n_y^2) = \frac{\hbar^2 \pi^2}{2mL^2} n^2 = E_n n^2$ Calculate the density of states, $g(E)$, for this 2-dimensional infinite square well potential carefully showing all your steps.

          Problem 3 (25 points)
2-dimensional density of states for a gas of particles: Assume there is a gas of particles
confined to a two-dimensional region of space which we can consider to be a square in which
each side has length $L$. The wavefunction and energy levels for the infinite two-dimensional
square well can be written as
$\psi(x,y) = A \sin(\frac{n_x \pi x}{L}) \sin(\frac{n_y \pi y}{L})$
$E = \frac{\hbar^2 \pi^2}{2mL^2} (n_x^2 + n_y^2) = \frac{\hbar^2 \pi^2}{2mL^2} n^2 = E_n n^2$
Calculate the density of states, $g(E)$, for this 2-dimensional infinite square well potential
carefully showing all your steps.

Problem 3 (25 points)
2-dimensional density of states for a gas of particles: Assume there is a gas of particles
confined to a two-dimensional region of space which we can consider to be a square in which
each side has length L. The wavefunction and energy levels for the infinite two-dimensional
square well can be written as
ψ(x,y) = A sin((nx π x)/(L)) sin((ny π y)/(L))
E = (ħ^2 π^2)/(2mL^2) (nx^2 + ny^2) = (ħ^2 π^2)/(2mL^2) n^2 = En n^2
Calculate the density of states, g(E), for this 2-dimensional infinite square well potential
carefully showing all your steps.

Added by Susan M.

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