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• Physics

# Heisenberg equation

The Heisenberg equation is the fundamental equation of quantum mechanics in the so-called Heisenberg formulation.

In quantum mechanics the observable physical quantities are quantified and are in the form of a hermitian operator $\hat A$ .

A particularly important operator is the Hamiltonian operator $\hat H$ defined from the total energy of the physical system under consideration, such as the hydrogen atom, an electron in a magnetic field etc.

The equation of motion of a physical quantity involves these operators and is written:

$\frac{d \hat A}{dt}=\frac{1}{i\hbar}[\hat A, \hat H]+\frac{\partial \hat A}{\partial t}$

where $[\hat A, \hat H]=\hat A \hat H - \hat H \hat A$ and $\hbar$ is the Planck constant divided by $2\pi$.

This is the Heisenberg equation.

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