Occupation Number

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Occupation Number


in quantum mechanics and quantum statistics, a number that indicates the extent to which quantum states are filled by the particles of a quantum-mechanical system consisting of many identical particles. For a system consisting of fermions, or particles with half-integral spin, the occupation numbers may take only two values: 0 for empty states or 1 for filled states. For a system consisting of bosons, or particles with integral spin, the occupation numbers may take any nonnegative .integral values: 0,1, 2,. . . For a given system, the sum of all occupation numbers should be equal to the number of particles in the system.

Occupation numbers may also be used to describe the numbers of elementary excitations, or quasiparticles, of quantum fields. In this case, the sum of the occupation numbers is not fixed.

The occupation numbers averaged over a state in statistical equilibrium for ideal quantum gases are specified by either the Fermi-Dirac or the Bose-Einstein distribution function [see equation (19) in STATISTICAL MECHANICS]. The concept of occupation numbers underlies the method of second quantization, which is also called the occupation-number representation.


The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
By assuming the neutrino occupation number associated with a given flavor (mode) as reference quantum number, one can establish the following correspondences with two-qubit states:
Analogously with the Pontecorvo states (5), we assume the neutrino occupation number as reference quantum number.
so that any occupation number (once divided by N) is bounded by:
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The experiment [7] would allow one to identify an additional quantum state if its occupation number would not be suppressed by more than a factor of 200 compared to that for other states.
[GRAPHIC OMITTED] Table 2.1 HIV infection is devastating some occupations in Zambia and Uganda Zambia HIV-positive Occupation Number (percent) Mid wives 379 39 Nurses 370 44 Office workers or teachers 370 42 Traditional birth attendants 369 12 Uganda HIV-positive Occupation Number (percent) Mid wives 373 21 Nurses 381 11 Office workers or teachers 371 18 Traditional birth attendants 375 5 Note: Based on surveys conducted during December 1991-January 1992.
TABLE 1 OCCUPATIONS POTENTIALLY AT RISK FOR CARPAL TUNNEL SYNDROME Occupation Number Employed* Computer operator 241,000 Data Key Entry Operator 324,000 Mail Handlers 317,000 Statistics Clerk 93,000 Grocery Checker 1,902,000 Typist 991,000 Carpenter 932,000 Musician 192,000 Barber 94,000 Cosmetologist 524,000 Electronic Assembler 144,000 * Source: U.S.
where t = T/B, u = U/B, S = 4[pi][a.sup.2.sub.0] N [R.sup.2]/[B.sup.2], [a.sub.0] is the Bohr radius (= 0.5292 A), R is the Rydberg energy (= 13.6057 eV), T is the incident electron energy, and N, B, and U are the electron occupation number, the binding energy, and the average kinetic energy of the orbital, respectively.
Over 4 years, neonatal intensive care unit bed occupation numbers increased from 8,302 to 15,625, and Dr.