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-141041)
- Kvantna i optička interferometrija (RS-141003)
- Alternativne teorije gravitacije (RS-141036)
DOI: 10.1088/1751-8113/42/23/235302
ISSN: 1751-8113