The free time of arrival problem in quantum phase space

Authors

  • Dean Alvin L. Pablico ⋅ 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 theory of time of arrival (TOA) operators provides a general framework for incorporating the arrival time of a particle as a quantum observable within the rigged Hilbert space formulation of quantum mechanics. In this paper, we introduce a non-operator-based formalism by considering the arrival time problem of a free structureless particle in quantum phase space. We derive the corresponding arrival time expectation value and eigenvalue equation and show that our results correctly lead to the well-known predictions of the theory of TOA operators. This paper then offers a possibility of developing an alternative formalism that resolves quantum time of arrival problems using only c-numbers and real-valued functions instead of non-commuting operators.

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Issue

Article ID

SPP-2023-2H-05

Section

Theoretical and Mathematical Physics

Published

2023-07-03

How to Cite

[1]
DAL Pablico and EA Galapon, The free time of arrival problem in quantum phase space, Proceedings of the Samahang Pisika ng Pilipinas 41, SPP-2023-2H-05 (2023). URL: https://proceedings.spp-online.org/article/view/SPP-2023-2H-05.