22. For a system, p is density distribution function, g; and p,; are coordinates and momenta
respectively. f represents number of degress of freedom. Which of the following does not
represent Liouville’s equation?

ap _ ३० | ५४ ३ ०५ | ap 4७ _
‏عو رق رو وو ےو )® ۷ م‎
೧ ೫,5 ap aH ap aH dp
൮൭ ൧2 op oH 0൧6൧ 0 Po
നാ നന്‌ 0) 2

23. If / represents density matrix and H represents Hamiltonian of the system, which of the
following statement is incorrect regarding density matrix?
(A) If system is in equilibrium, lA, ‏عم‎ 0
(B) Density matrix is diagonal in energy representation
(C) Density matrix is always diagonal in any representation

(D) The diagonal element of the matrix ,,,represents the probability for the system
to be found in state ®,,

24. Ifthe number density of a non-relativistic free electron gas in three dimension is increased
8 times, ground state pressure of the system will:

(ಸ) Increase by a factor of 32 (B)_ Increase by a factor of 8
(C) Decrease by a factor of 8 (D)_ Decrease by a factor of 2

25. Which of the following statement is incorrect regarding Bose Einstein condensation?

(A) The characteristic temperature T, for Bose Hinstein condensation depends only
on particle mass and particle density in the system

(B) Below characteristic temperature T;, all particles reside in the ground state
(C) In Bose-Einstein condensates, particles have overlapping wave functions

(D) Bose Einstein condensation is a second order phase transition

26. A classical one-dimensional system of non-interacting particles is under the influence of a
potential V(x)=ax*, where @ is a constant. What is the average potential energy of a

particle?
(ಯ ಸ? (3)
(C) 0)
A 7 084/2023

[P.T.0.]