**eV**and here I will explain the following topic:

# What is the Ehrenfest Theorem?

**Explanation**

## Video

In general, the Ehrenfest theorem states:

Here \( \hat{A} \) is any quantum mechanical operator and \( [\hat{H}, \hat{A}] \) is the commutator of the energy operator and the operator \( \hat{A} \). \( \langle\hat{A}\rangle \) is the mean value of the operator.

This quantum mechanical equation is *analogous* to the total time derivative of a *classical* function \( f(q,p,t) \) (with \(q,p,t\) being generalized coordinates in the Hamiltonian formalism):

Here, \( \{H,f\} \) is the **Poisson bracket** of the Hamilton function \( H \) and the function \( f \).