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Main Author: Mostafazadeh, Ali
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2404.01881
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author Mostafazadeh, Ali
author_facet Mostafazadeh, Ali
contents We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a time-independent Hilbert space. We show that in general the Hamiltonian operator does not represent an observable of the system even if it is a self-adjoint operator. This is related to a hidden geometric aspect of quantum mechanics arising from the presence of an operator-valued gauge potential. We also offer a careful treatment of quantum systems whose Hilbert space is obtained by endowing a time-independent vector space with a time-dependent inner product.
format Preprint
id arxiv_https___arxiv_org_abs_2404_01881
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Consistent treatment of quantum systems with a time-dependent Hilbert space
Mostafazadeh, Ali
Quantum Physics
General Relativity and Quantum Cosmology
Mathematical Physics
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a time-independent Hilbert space. We show that in general the Hamiltonian operator does not represent an observable of the system even if it is a self-adjoint operator. This is related to a hidden geometric aspect of quantum mechanics arising from the presence of an operator-valued gauge potential. We also offer a careful treatment of quantum systems whose Hilbert space is obtained by endowing a time-independent vector space with a time-dependent inner product.
title Consistent treatment of quantum systems with a time-dependent Hilbert space
topic Quantum Physics
General Relativity and Quantum Cosmology
Mathematical Physics
url https://arxiv.org/abs/2404.01881