Self-adjoint time operator is the rule for finite-dimensional bounded discrete Hamiltonians

Authors

  • Ralph Farrales ⋅ PH National Institute of Physics, University of the Philippines Diliman
  • Eric Galapon ⋅ PH National Institute of Physics, University of the Philippines Diliman

Abstract

Pauli’s theorem historically forbade the existence of operators canonically conjugate to a semibounded and discrete Hamiltonian. In recent years, this was disproven, and as a counterexample, it was shown that for every infinite-dimensional semibounded discrete Hamiltonian with some growth condition and constant degeneracy, there exists a characteristic self-adjoint operator canonically conjugate to it. In this paper, we extend it to the finite-dimensional case, and show that there always exists a characteristic self-adjoint time operator canonically conjugate to every finite-dimensional bounded discrete Hamiltonian.

Issue

Article ID

SPP-2024-PC-20

Section

Poster Session C (Theoretical and Mathematical Physics)

Published

2024-06-27

How to Cite

[1]
R Farrales and E Galapon, Self-adjoint time operator is the rule for finite-dimensional bounded discrete Hamiltonians, Proceedings of the Samahang Pisika ng Pilipinas 42, SPP-2024-PC-20 (2024). URL: https://proceedings.spp-online.org/article/view/SPP-2024-PC-20.