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Closed-system quantum evolution generated by a self-adjoint Hamiltonian through a unitary one-parameter group.
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Unitary quantum evolution is a strongly continuous one-parameter action by unitary operators; generic continuous-time dynamical systems need not be linear or unitary.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
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A self-adjoint Hamiltonian generates unitary time evolution.
A theory, law, or interaction describes the behavior of the target within a stated regime. The edge detail must state important limits or qualifications.
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For a self-adjoint time-independent Hamiltonian, the Schrödinger equation is the differential form of the strongly continuous unitary evolution . Time-dependent Hamiltonians require additional domain and well-posedness hypotheses.
Reinterpret an object, pass to an equivalent presentation, or relate canonically corresponding structures; the carrier may change.
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Stone’s theorem establishes the correspondence between strongly continuous one-parameter unitary groups and self-adjoint generators; it is a theorem about the formalism rather than the formalism itself.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
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Closed-system time evolution is represented by unitary operators.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
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