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College Physics

Symmetry and conserved quantity of time-dependent quantum system

Jing Xiao-gong

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

Symmetry of time-dependent quantum system is discussed.The criterion is given for proving the conservation of a time-dependent mechanic quantity.

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For time-dependent systems the wavefunction depends explicitly on time and it is not a pure state of the Hamiltonian. We construct operators for which the above wavefunction is a pure state. The method is based on the introduction of conserved quantities QQQ and the pure states are defined by Q^ψ=qψ{\hat Q}ψ=qψQ^​ψ=qψ. The conserved quantities are constructed using parametrised mechanics and the Noether theorem.
This work addresses the problem of causation in physics, as for quantum fields, the fundamental theory describing elementary particle physics. Three basic elements are used as methodological concepts: a) the notion of mass-point and the notion of a field (as quantum field) describing a physical system (both concepts are used in physics to characterize elementary particles); b) the notion of state of a mass-point and of a field; c) the notion of causality among states, which are defined by symmetries. Then time and space changes include a space-like causality. These elements are discussed by using the definition of measurement, associated with the notion of symmetry. The derived results give rise to a generalization of the concept of causality, since a mechanical system includes mass-points, fields, and systems composed of mass-points and fields, together. In addition, conserved quantities, founding some causality theories, are generalized due to the notion of symmetry associated with causality.