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POSTULATES OF QUANTUM STATISTICS
Postulates of quantum statistics
1.
Physical state of a quantum system is described by a column vector
(t ) whose components are probability amplitudes of states in which
system can be found. No. of states are equal to the dimension of Hilbert
space, which can be finite/infinite.
2.
(t ) must be a unit vector. Ie.,
(t ) (t )  1 .
3.
Physical observables are represented by linear, hermitian operators that
act on the vectors of Hilbert space.
4.
Measurement of an observable A will yield one of the eigen values of A.
ie., A a i  ai a i
5.
Time evolution of the state vector is given by Schrodinger equation
i

 H
t
Evolution is governed by the unitary operator
exp(iHt / ) .
6.
If two operators A and B are not commuting, then their simultaneous
measurement will have an uncertainty, governed by uncertainty
principle.
7.
Particles are indistinguishable in the sense that even though they change
positions, it will not reflect in the macroscopic properties of system.
8.
Particles obey spin statistics theorem, those ones with integral spins are
called as bosons, while other ones with half integer spins are called as
fermions.
9.
Any no. of bosons can be sent to an energy level, but only single fermion
can find its space there.