Physically, these matrices can be thought of as raising operators acting on a Hilbert space of " n " identical fermions in the occupation number basis.
12.
Thus when we count the number of possible states of the system, we must count each and every microstate, and not just the possible sets of occupation numbers.
13.
While the occupation numbers are unchanged, nevertheless there is change in the energy levels of one-to-one corresponding, pre-and post-compression, eigenstates.
14.
The number of ways that a set of occupation numbers \ displaystyle n _ i can be realized is the product of the ways that each individual energy level can be populated:
15.
By 1823 population had increased to 139, including four farmers and a Tuesday carrier to Hull; occupation numbers had not changed by 1851, although population had dropped to 103.
16.
On the other hand, in quantum theory, if a perturbative element of compressive work is done rapidly, it randomly changes the occupation numbers of the eigenstates, as well as changing their shapes.
17.
The number of ways that a set of occupation numbers " n " " i " can be realized is the product of the ways that each individual energy level can be populated:
18.
The bonding NBOs are of the " Lewis orbital "-type ( occupation numbers near 2 ); antibonding NBOs are of the " non-Lewis orbital "-type ( occupation numbers near 0 ).
19.
The bonding NBOs are of the " Lewis orbital "-type ( occupation numbers near 2 ); antibonding NBOs are of the " non-Lewis orbital "-type ( occupation numbers near 0 ).
20.
Where (-1 ) ^ { \ sum _ { \ beta is called the Jordan-Wigner string, which depends on the ordering of the involved single-particle states and adding the fermion occupation numbers of all preceding states.
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