Question

1. Which couple of assertions relates to quantum statistics?
   (a) Probability density function is a function of coordinates and momenta of all particles; infinite time is needed to measure positions of all energy levels.
   (b) Initial conditions cannot be determined simultaneously for all particles; system’s state is described by coordinates and momenta (in phase space).
   (c) It is impossible to determine the quantum states with certain energy (stationary levels); system’s state is set by the value of system’s energy, but not by coordinates and momenta.
   (d) Number of states is proportional to the volume of phase space; probability of state is proportional to the diagonal element of the density matrix.

Answer 1

(C) and (D) relates to quantum statistics.

In quantum, one cannot determine position and momenta simultaneously (Heisenberg uncertainty principle), so the first two options can't relate to the quantum statistics.

In quantum statistics, we can't measure or determine the state (energy) but find the probabilty of system in a particluar state (C). Also, number of sates are proportional to the volume of phase space and the probabilty of state is diagonal element of density matrix (D).