General form of separable potentials leading to exact closed-form solution of the time kernel equation

Authors

  • Carl A. L. Arguelles ⋅ PH Theoretical Physics Group, National Institute of Physics, University of the Philippines Diliman
  • Dean Alvin L. Pablico ⋅ PH Theoretical Physics Group, National Institute of Physics, University of the Philippines Diliman
  • Eric A. Galapon ⋅ PH Theoretical Physics Group, National Institute of Physics, University of the Philippines Diliman

Abstract

In investigating time-of-arrival observables (TOA) that are canonically conjugate to the Hamiltonian, an exact closed-form expression will be of inevitable necessity. We have previously derived such expression but is only applicable for a class of potentials we refer to as separable potentials. In this paper, we derive the necessary form separable potentials must assume. We found that they must be a superposition of linearly independent exponential functions and some constant. This provides an explicit closed-form formula valid for potentials with said form.

Issue

Article ID

SPP-2024-PC-14

Section

Poster Session C (Theoretical and Mathematical Physics)

Published

2024-06-26

How to Cite

[1]
CAL Arguelles, DAL Pablico, and EA Galapon, General form of separable potentials leading to exact closed-form solution of the time kernel equation, Proceedings of the Samahang Pisika ng Pilipinas 42, SPP-2024-PC-14 (2024). URL: https://proceedings.spp-online.org/article/view/SPP-2024-PC-14.