Author Archives: Eric A. Galapon

R.J.C. Bagunu and E.A. Galapon, “Quantization of the Hamilton Equations of Motion,” arXiv:2409.03348

By | September 19, 2024
0 Comment

One of the fundamental problems in quantum mechanics is finding the correct quantum image of a classical observable that would correspond to experimental measurements. We investigate for the appropriate quantization rule that would yield a Hamiltonian that obeys the quantum analogue of Hamilton’s equations of motion, which includes differentiation of operators with respect to another… Read More »

R.A.E. Farrales and E.A. Galapon, “Characteristic time operators as quantum clocks,” arXiv:2409.03364

By | September 19, 2024
0 Comment

We consider the characteristic time operator T introduced in [E. A. Galapon, Proc. R. Soc. Lond. A, 458:2671 (2002)] which is bounded and self-adjoint. For a semibounded discrete Hamiltonian H with some growth condition, T satisfies the canonical relation [T,H]|ψ⟩=iℏ|ψ⟩ for |ψ⟩ in a dense subspace of the Hilbert space. While T is not covariant,… 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
0 Comment

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
0 Comment

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 »

P.C.M. Flores, D.A.L. Pablico and E.A. Galapon, “Partial and full tunneling processes across potential barriers,” EPL (2024)

By | March 9, 2024
0 Comment

We introduce the concept of partial-tunneling and full-tunneling processes to explain the seemingly contradictory non-zero and vanishing tunneling times often reported in the literature. Our analysis starts by considering the traversal time of a quantum particle through a potential barrier, including both above and below-barrier traversals, using the theory of time-of-arrival operators. We then show… Read More »

C.D. Tica, P.J. Blancas and E.A. Galapon, “Exact Evaluation and extrapolation of the divergent expansion for the Heisenberg-Euler Lagrangian II: Non-alternating Case,” https://arxiv.org/abs/2402.14839

By | March 9, 2024
0 Comment

We applied the method of finite-part integration [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to evaluate in closed-form the exact one-loop integral representations of the Heisenberg-Euler Lagrangian from QED for a constant electric field and electric-like self-dual background. We also devise a prescription based on the finite-part integration of the Cauchy principal value integral to sum… Read More »

C.D. Tica and E.A. Galapon, “Exact evaluation and extrapolation of the divergent expansion for the Heisenberg-Euler Lagrangian I: Alternating Case,” https://arxiv.org/abs/2310.08199

By | March 9, 2024
0 Comment

We applied the method of finite-part integration [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to evaluate in closed-form the exact one-loop integral representations of the Heisenberg-Euler Lagrangian from QED for a constant magnetic field and magnetic-like self-dual background. We also devise a prescription based on the finite-part integration of a generalized Stieltjes integral to sum and… Read More »

C.D. Tica and E.A. Galapon, “Summation and Extrapolation of Divergent Perturbation Series with logarithmic non-pertubative behavior,” https://arxiv.org/abs/2310.08199

By | November 1, 2023
0 Comment

We devise a prescription based on the finite-part integration of the generalized Stieltjes integral [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to sum the associated divergent series of Stieltjes across all asymptotic regimes. The prescription utilizes the divergent negative-power moments which we treated as Hadamard’s finite part integrals to transform the divergent weak-field perturbation expansions for… Read More »