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If the energy dispersion of a two-dimensional electron system is E = uħk where u is the velocity and k is the momentum, then the density of states D(E) depends on the energy as 
  • a)
    1/√E
  • b)
    √E
  • c)
    E
  • d)
    constant
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If the energy dispersion of a two-dimensional electron system is E = u...
In two dimensional system, the number of allowed k-states in range k and k + dk is

Given dispersion relation is 

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If the energy dispersion of a two-dimensional electron system is E = u...
The density of states D(E) for a two-dimensional electron system with energy dispersion E = uk is given by:

D(E) = A / |dE/dk|

where A is a constant and dE/dk is the derivative of energy with respect to momentum.

In this case, E = uk, so we can differentiate both sides of the equation with respect to k:

dE/dk = u

Substituting this back into the expression for D(E), we get:

D(E) = A / |u|

Since u is a constant, the absolute value of u is also a constant. Therefore, the density of states D(E) is independent of the energy E. So the correct answer is:

a) 1/
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If the energy dispersion of a two-dimensional electron system is E = uk where u is the velocity and k is the momentum, then the density of states D(E) depends on the energy asa)1/√Eb)√Ec)Ed)constantCorrect answer is option 'C'. Can you explain this answer?
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