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The Schrödinger-picture evolution equation ; its concrete Hamiltonian may describe a nonrelativistic system or an effective quantum theory.
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This is an authored directed relation from the source endpoint to the target endpoint.
The nonrelativistic kinetic term is proportional to the Laplacian in position representation.
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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The Schrödinger equation is a linear partial differential equation in common coordinate representations, with coefficients and domain fixed by the Hamiltonian and physical boundary conditions.
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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For spin-independent interactions or after suppressing spin terms, the Pauli equation reduces to Schrödinger dynamics.
The target is recovered from the source either in a stated mathematical or asymptotic limit, or through a quantitatively controlled approximation with identified small parameters or omitted terms. The edge label and detail must state which case applies and its regime of validity.
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This is an authored directed relation from the source endpoint to the target endpoint.
A periodic-electron model uses the nonrelativistic Schrödinger eigenvalue problem with a lattice-periodic one-particle or mean-field Hamiltonian. Correlation, relativistic, disorder, and lattice-motion effects require extensions or different effective descriptions.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
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The Schrödinger equation supplies the state-evolution law for the Schrödinger-picture formulation of nonrelativistic quantum mechanics; it is not the universal evolution equation of all quantum theories.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
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Solving the Schrödinger equation across a barrier gives reflected and transmitted amplitudes, with semiclassical formulas valid only when their stated action and smoothness conditions hold.
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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