Subtle inconsistencies in the straightforward definition of the logarithmic function of annihilation and creation operators and a way to avoid them
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2009
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Using the resolution of identity spanned by coherent states of the harmonic oscillator, any entire function of the creation and the annihilation operators and its action on a vector in Hilbert space can be defined directly and simply. We show that such a direct approach applied to non-entire functions ln (a) over cap and ln (a) over cap (dagger), present in the literature, may lead to errors and contradictions. We elucidate their roots and propose a way to avoid them. We discuss the obtained results.
Izvor:
Journal of Physics A-Mathematical and Theoretical, 2009, 42, 23Finansiranje / projekti:
- Zaštita od zračenja-fundamentalni, teorijski i eksperimentalni fizički aspekti (RS-MESTD-MPN2006-2010-141041)
- Kvantna i optička interferometrija (RS-MESTD-MPN2006-2010-141003)
- Alternativne teorije gravitacije (RS-MESTD-MPN2006-2010-141036)
DOI: 10.1088/1751-8113/42/23/235302
ISSN: 1751-8113
WoS: 000266287500011
Scopus: 2-s2.0-70449506537
Kolekcije
Institucija/grupa
GraFarTY - JOUR AU - Davidović, Ljubica D. AU - Arsenović, Dušan AU - Davidović, Milena AU - Davidović, Dragomir M. PY - 2009 UR - https://grafar.grf.bg.ac.rs/handle/123456789/269 AB - Using the resolution of identity spanned by coherent states of the harmonic oscillator, any entire function of the creation and the annihilation operators and its action on a vector in Hilbert space can be defined directly and simply. We show that such a direct approach applied to non-entire functions ln (a) over cap and ln (a) over cap (dagger), present in the literature, may lead to errors and contradictions. We elucidate their roots and propose a way to avoid them. We discuss the obtained results. T2 - Journal of Physics A-Mathematical and Theoretical T1 - Subtle inconsistencies in the straightforward definition of the logarithmic function of annihilation and creation operators and a way to avoid them IS - 23 VL - 42 DO - 10.1088/1751-8113/42/23/235302 ER -
@article{ author = "Davidović, Ljubica D. and Arsenović, Dušan and Davidović, Milena and Davidović, Dragomir M.", year = "2009", abstract = "Using the resolution of identity spanned by coherent states of the harmonic oscillator, any entire function of the creation and the annihilation operators and its action on a vector in Hilbert space can be defined directly and simply. We show that such a direct approach applied to non-entire functions ln (a) over cap and ln (a) over cap (dagger), present in the literature, may lead to errors and contradictions. We elucidate their roots and propose a way to avoid them. We discuss the obtained results.", journal = "Journal of Physics A-Mathematical and Theoretical", title = "Subtle inconsistencies in the straightforward definition of the logarithmic function of annihilation and creation operators and a way to avoid them", number = "23", volume = "42", doi = "10.1088/1751-8113/42/23/235302" }
Davidović, L. D., Arsenović, D., Davidović, M.,& Davidović, D. M.. (2009). Subtle inconsistencies in the straightforward definition of the logarithmic function of annihilation and creation operators and a way to avoid them. in Journal of Physics A-Mathematical and Theoretical, 42(23). https://doi.org/10.1088/1751-8113/42/23/235302
Davidović LD, Arsenović D, Davidović M, Davidović DM. Subtle inconsistencies in the straightforward definition of the logarithmic function of annihilation and creation operators and a way to avoid them. in Journal of Physics A-Mathematical and Theoretical. 2009;42(23). doi:10.1088/1751-8113/42/23/235302 .
Davidović, Ljubica D., Arsenović, Dušan, Davidović, Milena, Davidović, Dragomir M., "Subtle inconsistencies in the straightforward definition of the logarithmic function of annihilation and creation operators and a way to avoid them" in Journal of Physics A-Mathematical and Theoretical, 42, no. 23 (2009), https://doi.org/10.1088/1751-8113/42/23/235302 . .