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
0 Comment

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
0 Comment

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 »

E.A. Galapon, “Regularized limit, analytic continuation and finite-part integration,” https://arxiv.org/abs/2108.02013

By | March 4, 2022
0 Comment

Finite-part integration is a recent method of evaluating a convergent integral in terms of the finite-parts of divergent integrals deliberately induced from the convergent integral itself [E. A. Galapon, Proc. R. Soc., A 473, 20160567 (2017)]. Within the context of finite-part integration of the Stieltjes transform of functions with logarithmic growths at the origin, the… Read More »

L. Villanueva and E.A. Galapon, “Finite-part integration in the presence of competing singularities: Transformation equations for the hypergeometric functions arising from finite-part integration”

By | December 5, 2020
0 Comment

Finite-part integration is a recently introduced method of evaluating convergent integrals by means of the finite part of divergent integrals [E.A. Galapon, {\it Proc. R. Soc. A 473, 20160567} (2017)]. Current application of the method involves exact and asymptotic evaluation of the generalized Stieltjes transform under the assumption that the extension of in the complex… Read More »

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

By | August 12, 2019
0 Comment

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 »

C.D. Tica and E.A. Galapon, “Finite-part integration of the generalized Stieltjes transform and its dominant asymptotic behavior for small values of the parameter. II. Non-integer orders”, Journal of Mathematical Physics 60, 013502 (2019).

By | January 3, 2019
0 Comment

Get your copy here from the publisher. Compare with the original version of the paper, especially Section 3. Tica-Galapon Journal of Mathematical Physics 60, 013502 (2019) (accepted version)

The limit to infinity: Addendum to “The problem of missing terms in term by term integration involving divergent integrals”

By | December 29, 2018
0 Comment

In (Galapon 2017) we considered the problem of missing terms arising from evaluating the incomplete Stieltjes transform, (1)   following from binomially expanding the kernel about and then integrating the resulting infinite series term by term. The interchange of summation and integration leads to the infinite series whose terms are divergent integrals. Assigning values to… Read More »