Subtle inconsistencies in the straightforward definition of the logarithmic function of annihilation and creation operators and a way to avoid them
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.
Source:
Journal of Physics A-Mathematical and Theoretical, 2009, 42, 23Funding / projects:
- 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
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Institution/Community
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 . .