Related papers: Consistent treatment of quantum systems with a time-dependent Hilbert space

Consistent treatment of quantum systems with a time-dependent Hilbert space

URL: http://arxiv.org/abs/2404.01881v1
Date: Tue, 2 Apr 2024 12:13:56 GMT
Title: Consistent treatment of quantum systems with a time-dependent Hilbert space
Authors: Ali Mostafazadeh,
Abstract summary: 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.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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.

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