Quasi-Hermitian operators in quantum mechanics and the variational principle
We establish a general criterion for a set of non-Hermitian operators to constitute a consistent quantum mechanical system, which allows for the normal quantum-mechanical interpretation. This involves the construction of a metric (if it exists) for the given set of non-Hermitian observables. We disc...
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| Published in | Annals of physics Vol. 213; no. 1; pp. 74 - 101 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier Inc
1992
Elsevier |
| Subjects | |
| Online Access | Get full text |
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| Abstract | We establish a general criterion for a set of non-Hermitian operators to constitute a consistent quantum mechanical system, which allows for the normal quantum-mechanical interpretation. This involves the construction of a metric (if it exists) for the given set of non-Hermitian observables. We discuss uniqueness of this metric. We also show that it is not always necessary to construct the metric for the whole set of observables under consideration, but that it is sufficient for some calculational purposes to construct it for a subset only, even though this metric is, in general, not unique. The restricted metric turns out to be particularly useful in the implementation of a variational principle, which we also formulate. |
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| AbstractList | We establish a general criterion for a set of non-Hermitian operators to constitute a consistent quantum mechanical system, which allows for the normal quantum-mechanical interpretation. This involves the construction of a metric (if it exists) for the given set of non-Hermitian observables. We discuss uniqueness of this metric. We also show that it is not always necessary to construct the metric for the whole set of observables under consideration, but that it is sufficient for some calculational purposes to construct it for a subset only, even though this metric is, in general, not unique. The restricted metric turns out to be particularly useful in the implementation of a variational principle, which we also formulate. |
| Author | Hahne, F.J.W. Scholtz, F.G. Geyer, H.B. |
| Author_xml | – sequence: 1 givenname: F.G. surname: Scholtz fullname: Scholtz, F.G. – sequence: 2 givenname: H.B. surname: Geyer fullname: Geyer, H.B. – sequence: 3 givenname: F.J.W. surname: Hahne fullname: Hahne, F.J.W. |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=5088844$$DView record in Pascal Francis |
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| CODEN | APNYA6 |
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| Cites_doi | 10.1016/0029-5582(65)90862-X 10.1016/0370-2693(87)91037-9 10.1103/PhysRevC.38.2450 10.1016/0375-9474(71)90122-9 10.1016/0003-4916(72)90315-6 10.1063/1.528066 10.1103/PhysRevC.23.2305 10.1103/RevModPhys.63.375 10.1016/0375-9474(89)90292-3 10.1016/0003-4916(73)90044-4 |
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| References | Richtmyer (BIB1) 1978; Vol. 1 Schechter (BIB2) 1981 Klein, Marshalek (BIB4) 1991; 63 Glimm, Jaffe (BIB11) 1981 Bratteli, Robinson (BIB10) 1987; Vols. 1, 2 Rowe, Le Blanc, Hecht (BIB17) 1988; 29 Hecht (BIB18) 1987 Lipkin, Meshkov, Glick (BIB13) 1965; 62 Takada (BIB16) 1988; 38 Janssen, Schuck (BIB7) 1989; 501 Schucan, Weidenmüller, Schucan, Weidenmüller (BIB5) 1973; 73 Kato (BIB19) 1966 (BIB6) 1975; Vol. 40 Pease (BIB8) 1965 Hahne (BIB15) 1981; 23 Cambiaggio, Dukelsky (BIB12) 1987; 197 Streater, Wightman (BIB9) 1964 Gupta (BIB14) 1977 Janssen, Dönau, Frauendorf, Jolos (BIB3) 1971; 172 Hecht (10.1016/0003-4916(92)90284-S_BIB18) 1987 Richtmyer (10.1016/0003-4916(92)90284-S_BIB1) 1978; Vol. 1 (10.1016/0003-4916(92)90284-S_BIB6) 1975; Vol. 40 Rowe (10.1016/0003-4916(92)90284-S_BIB17) 1988; 29 Bratteli (10.1016/0003-4916(92)90284-S_BIB10) 1987; Vols. 1, 2 Hahne (10.1016/0003-4916(92)90284-S_BIB15) 1981; 23 Schucan (10.1016/0003-4916(92)90284-S_BIB5_2) 1973; 76 Glimm (10.1016/0003-4916(92)90284-S_BIB11) 1981 Cambiaggio (10.1016/0003-4916(92)90284-S_BIB12) 1987; 197 Pease (10.1016/0003-4916(92)90284-S_BIB8) 1965 Janssen (10.1016/0003-4916(92)90284-S_BIB7) 1989; 501 Gupta (10.1016/0003-4916(92)90284-S_BIB14) 1977 Schechter (10.1016/0003-4916(92)90284-S_BIB2) 1981 Klein (10.1016/0003-4916(92)90284-S_BIB4) 1991; 63 Takada (10.1016/0003-4916(92)90284-S_BIB16) 1988; 38 Kato (10.1016/0003-4916(92)90284-S_BIB19) 1966 Lipkin (10.1016/0003-4916(92)90284-S_BIB13) 1965; 62 Schucan (10.1016/0003-4916(92)90284-S_BIB5_1) 1973; 73 Streater (10.1016/0003-4916(92)90284-S_BIB9) 1964 Janssen (10.1016/0003-4916(92)90284-S_BIB3) 1971; 172 |
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| Snippet | We establish a general criterion for a set of non-Hermitian operators to constitute a consistent quantum mechanical system, which allows for the normal... |
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| Title | Quasi-Hermitian operators in quantum mechanics and the variational principle |
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