Category Archives: Time in Quantum Mechanics

P.C.M. Flores, D.A.L Pablico and E.A. Galapon, “Instantaneous tunneling time within the theory of time-of-arrival operators,” arXiv:2409.12389

By | September 22, 2024
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It has been shown in \href{this https URL}{\textit{Phys. Rev. Lett.}, \textbf{108} 170402 (2012)}, that quantum tunneling is instantaneous using a time-of-arrival (TOA) operator constructed by Weyl quantization of the classical TOA. However, there are infinitely many possible quantum images of the classical TOA, leaving it unclear if one is uniquely preferred over the others. This… Read More »

D.A.L. Pablico, J.J.P. Magadan, C.A.L Arguelles and E.A. Galapon, “The role of conjugacy in the dynamics of time of arrival operators,” Physics Letters A 523, 129778 (2024)

By | September 3, 2024
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Abstract The construction of time of arrival (TOA) operators canonically conjugate to the system Hamiltonian entails finding the solution of a specific second-order partial differential equation called the time kernel equation (TKE). In this paper, we provide an exact analytic solution of the TKE for a special class of potentials satisfying a specific separability condition.… Read More »

D.A.L. Pablico, J.J.P. Magadan, C.L. Arguelles and E.A. Galapon, “The role of conjugacy in the dynamics of time of arrival operators,” arXiv:2404.16298

By | April 27, 2024
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The role of conjugacy in the dynamics of time of arrival operators The construction of time of arrival (TOA) operators canonically conjugate to the system Hamiltonian entails finding the solution of a specific second-order partial differential equation called the time kernel equation (TKE). An expanded iterative solution of the TKE has been obtained recently in… Read More »

D.A.L. Pablico and E.A. Galapon, “Moyal deformation of the classical time of arrival,” https://arxiv.org/abs/2309.00222

By | November 1, 2023
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The quantum time of arrival (TOA) problem requires statistics of the measured arrival times given only the initial state of a particle. Following the standard framework of quantum theory, the problem translates into finding an appropriate quantum image of the classical arrival time , usually in operator form . In this paper, we consider the… Read More »

P.C.M. Flores and E.A. Galapon, “Instantaneous tunneling of relativistic massive spin-0 particles,” https://arxiv.org/abs/2207.09040

By | July 20, 2022
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The tunneling time problem earlier studied in \href{https://link.aps.org/doi/10.1103/PhysRevLett.108.170402}{Phys. Rev. Lett. \textbf{108}, 170402 (2012)} using a non-relativistic time-of-arrival (TOA) operator predicted that tunneling time is instantaneous implying that the wavepacket becomes superluminal below the barrier. The non-relativistic treatment raises the question whether the superluminal behavior is a mere non-relativistic phenomenon or an an inherent quantum effect… Read More »

D.A.L. Pablico and E.A. Galapon, “Quantum corrections to the Weyl quantization of the classical time of arrival,” https://arxiv.org/abs/2205.08694

By | May 19, 2022
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A time of arrival (TOA) operator that is conjugate with the system Hamiltonian was constructed by Galapon without canonical quantization in [J. Math. Phys. \textbf{45}, 3180 (2004)]. The constructed operator was expressed as an infinite series but only the leading term was investigated which was shown to be equal to the Weyl-quantized TOA-operator for entire… Read More »

P.C.M Flores and E.A. Galapon, “Relativistic free motion time of arrival operator for massive spin-0 particles with positive energy,” https://arxiv.org/abs/2203.00898

By | March 4, 2022
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A relativistic version of the Aharonov-Bohm time of arrival operator for spin-0 particles was constructed by Razavi in [Il Nuovo Cimento B \textbf{63}, 271 (1969)]. We study the operator in detail by taking its rigged Hilbert space extension. It is shown that the rigged Hilbert space extension of the operator provides more insights into the… Read More »

R.A.E. Farrales, H.B. Domingo and E.A. Galapon, “Conjugates to One Particle Hamiltonians in 1-Dimension in Differential Form,” https://arxiv.org/abs/2201.05777

By | March 4, 2022
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A time operator is a Hermitian operator that is canonically conjugate to a given Hamiltonian. For a particle in 1-dimension, a Hamiltonian conjugate operator in position representation can be obtained by solving a hyperbolic second-order partial differential equation, known as the time kernel equation, with some boundary conditions. One possible solution is the time of… Read More »

D.A.L. Pablico and E.A. Galapon, “Quantum traversal time across a potential well,” arXiv: 1908.03400

By | August 12, 2019
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Abstract We consider the quantum traversal time of an incident wave packet across a potential well using the theory of quantum time of arrival (TOA)-operators. This is done by constructing the corresponding TOA-operator across a potential well via quantization. The expectation value of the potential well TOA-operator is compared to the free particle case for… Read More »

What could have we been missing while Pauli’s Theorem was enforced?

By | May 23, 2016
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This post is the online version of the write-up of the contributed talk I gave at the Time and Matter Colloquium held at Venice on August 11-17, 2002 at the Venice International University. It is part of the proceedings of the Colloquim published by World Scientific. Abstract Pauli’s theorem asserts that the canonical commutation relation… Read More »