Space of State Vectors in PT Symmetrical Quantum Mechanics
Quantum Physics
2008-11-26 v2 High Energy Physics - Theory
Abstract
Space of states of PT symmetrical quantum mechanics is examined. Requirement that eigenstates with different eigenvalues must be orthogonal leads to the conclusion that eigenfunctions belong to the space with an indefinite metric. The self consistent expressions for the probability amplitude and average value of operator are suggested. Further specification of space of state vectors yield the superselection rule, redefining notion of the superposition principle. The expression for the probability current density, satisfying equation of continuity and vanishing for the bound state, is proposed.
Keywords
Cite
@article{arxiv.quant-ph/0104077,
title = {Space of State Vectors in PT Symmetrical Quantum Mechanics},
author = {G. S. Japaridze},
journal= {arXiv preprint arXiv:quant-ph/0104077},
year = {2008}
}
Comments
Revised version, explicit expressions for average values and probability amplitude added