Quantum time of arrival for the harmonic oscillator using the simplest symmetrization rule

  • Ramon Jose Cavitana Bagunu Department of Physical Sciences and Mathematics, University of the Philippines Manila
  • Eric Alvarez Galapon National Institute of Physics, University of the Philippines Diliman

Abstract

The quantum time of arrival for the harmonic oscillator Hamiltonian was obtained using the canonical commutation relation [H,T]=iI, where H is the Hamiltonian and T is the time of arrival operator. This was done using the basis operators Sm,n  from the simplest symmetrization rule, one of the different ordering rules along with Weyl and Born-Jordan ordering. The obtained time of arrival was found to be equivalent to the operator
resulting from Weyl quantization. The resulting time kernels are also equal, regardless of whether simplest symmetric or Weyl quantization is used.

Published
2020-09-11
How to Cite
[1]
R. J. Bagunu and E. Galapon. Quantum time of arrival for the harmonic oscillator using the simplest symmetrization rule, Proceedings of the Samahang Pisika ng Pilipinas 38, SPP-2020-2G-04 (2020). URL: https://paperview.spp-online.org/proceedings/article/view/SPP-2020-2G-04.
Section
2G/5A Theoretical and Mathematical Physics (Short Presentations)