# Matrix element (physics)

In physics, particularly in quantum perturbation theory, the **matrix element** refers to the linear operator of a modified Hamiltonian using Dirac notation.

The matrix element considers the effect of the newly modified Hamiltonian (i.e. the linear superposition of the unperturbed Hamiltonian plus interaction potential) on the quantum state.

Matrix elements are important in atomic, nuclear and particle physics.

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