Holomorphic Functional Calculus approach to the Characteristic Function of Quantum Observables
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913416479768576 |
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| author | Boukas, Andreas |
| author_facet | Boukas, Andreas |
| contents | We show how Cauchy's Integral Formula and the ideas of Dunford's Holomorphic Functional Calculus (for unbounded operators) can be used to compute the Vacuum Characteristic Function (Quantum Fourier Transform) of quantum random variables defined as self-adjoint operators on $L^2(\mathbb{R},\mathbb{C})$. We consider in detail several quantum observables defined in terms of the position and momentum operators $X$, $P$, respectively, on $L^2(\mathbb{R},\mathbb{C})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03694 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Holomorphic Functional Calculus approach to the Characteristic Function of Quantum Observables Boukas, Andreas Mathematical Physics Functional Analysis Spectral Theory Primary 47B25, 47B15, 47B40, 47A10, 81Q10, 81Q12, Secondary 47B47, 81S05 We show how Cauchy's Integral Formula and the ideas of Dunford's Holomorphic Functional Calculus (for unbounded operators) can be used to compute the Vacuum Characteristic Function (Quantum Fourier Transform) of quantum random variables defined as self-adjoint operators on $L^2(\mathbb{R},\mathbb{C})$. We consider in detail several quantum observables defined in terms of the position and momentum operators $X$, $P$, respectively, on $L^2(\mathbb{R},\mathbb{C})$. |
| title | Holomorphic Functional Calculus approach to the Characteristic Function of Quantum Observables |
| topic | Mathematical Physics Functional Analysis Spectral Theory Primary 47B25, 47B15, 47B40, 47A10, 81Q10, 81Q12, Secondary 47B47, 81S05 |
| url | https://arxiv.org/abs/2407.03694 |