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Moyal deformation of the classical arrival time | | Dean Alvin L. Pablico
; Eric A. Galapon
; | | Date: |
1 Sep 2023 | | Abstract: | The quantum time of arrival (TOA) problem requires a statistics of measured
arrival times given only a particle’s initial state. Following the standard
framework of quantum theory, the problem translates into finding an appropriate
quantum image of the classical arrival time $mathcal{T}_C(q,p)$, usually in
operator form $hat{mathrm{T}}$. In this paper, we consider the problem anew
within the phase space formulation of quantum mechanics. The resulting quantum
image is a real-valued and time-reversal symmetric function
$mathcal{T}_M(q,p)$ in formal series of $hbar^2$ with the classical arrival
time as the leading term. It is obtained from the Moyal bracket relation with
the system Hamiltonian and is hence interpreted as a Moyal deformation of the
classical TOA. Finally, we show that $mathcal{T}_M(q,p)$ is isomorphic to the
rigged Hilbert space TOA operator constructed recently in [Eur. Phys. J. Plus
extbf{138}, 153 (2023)] independent of canonical quantization. | | Source: | arXiv, 2309.00222 | | Services: | Forum | Review | PDF | Favorites | |
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