Quantum time transition states

Authors

Roland Christopher F. Caballar ⋅ PH National Institute of Physics, University of the Philippines Diliman
Eric A. Galapon ⋅ PH National Institute of Physics, University of the Philippines Diliman

Abstract

We show that for a particle spatially confined in a potential-free segment of the real line, there exists a self-adjoint time operator, known as the Characteristic Time Operator (CTO), which forms a dense canonical pair with the Hamiltonian corresponding to the system. The CTO can be interpreted in terms of the internal dynamics of the system, as follows: it is an operator whose eigenfunctions corrsponding to small-magnitude eigenvalues evolve in such a way that they make transitions to other CTO eigenfunctions which also correspond to small-magnitude eigenvalues. We compare the dynamical behavior of the CTO with the dynamical behavior of the self-adjoint Confined Quantum Time of Arrival (CTOA) operator corresponding to the system, which forms a closed canonical pair with the Hamiltonian.

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Issue

2007: Proceedings of the 25th Samahang Pisika ng Pilipinas Physics Congress

Article ID

SPP-2007-1B-02

Section

Theoretical Physics

Published

2007-10-24

How to Cite

[1]

RCF Caballar and EA Galapon, Quantum time transition states, Proceedings of the Samahang Pisika ng Pilipinas 25, SPP-2007-1B-02 (2007). URL: https://proceedings.spp-online.org/article/view/SPP-2007-1B-02.