# Correspondence rule

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This article is about correspondence rules in quantum physics. For their role in philosophy of science, see Carnap–Ramsey sentence.

In quantum mechanics, correspondence rules govern the principle of replacing physical quantities with operators.

Such replacements include energy and momentum, which can be derived informally from taking the time and space derivities of the plane wave function. These show a similarity to the heisenberg uncertainty principle.

Examples of correspondence rules

quantity operator See equation
Energy (Hamiltonian) ${\displaystyle i\hbar {\frac {\partial }{\partial t}}}$ Sc
Momentum ${\displaystyle -i\hbar \nabla }$ Continuity equation