Construction and dynamics of algebra-preserving time of arrival operators

Authors

  • Dean Alvin L. Pablico ⋅ PH National Institute of Physics, University of the Philippines Diliman
  • John Jaykel P. Magadan ⋅ PH National Institute of Physics, University of the Philippines Diliman
  • Carl Anthony L. Arguelles ⋅ PH National Institute of Physics, University of the Philippines Diliman
  • Eric A. Galapon ⋅ PH National Institute of Physics, University of the Philippines Diliman

Abstract

The construction of algebra-preserving time of arrival (APTOA) operators for nonlinear potentials has been a longstanding challenge in the theory of supraquantization. In this paper, we construct such an operator using a sinusoidal potential. The construction is facilitated by solving the associated time kernel equation (TKE) in closed-form using a specific separability condition. We then demonstrate numerically that the APTOA operator's eigenfunctions have the desired unitary arrival property, linking TOA measurements and the appearance of the incident particle at the arrival point. Finally, we show that the same operator exhibits sharper unitary dynamics compared to a non-algebra-preserving operator derived from Weyl quantization of the classical arrival time.

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Article ID

SPP-2024-1H-04

Section

Theoretical and Mathematical Physics

Published

2024-06-26

How to Cite

[1]
DAL Pablico, JJP Magadan, CAL Arguelles, and EA Galapon, Construction and dynamics of algebra-preserving time of arrival operators, Proceedings of the Samahang Pisika ng Pilipinas 42, SPP-2024-1H-04 (2024). URL: https://proceedings.spp-online.org/article/view/SPP-2024-1H-04.