# Calculate the expectation value of V from Ehrenfest's theorem

In summary, Ehrenfest's theorem is a mathematical theorem in quantum mechanics that relates the time evolution of a quantum system to the expectation value of its observables. It can be used to calculate the expectation value of V by solving the equation d⟨V⟩/dt = ⟨[V, H]⟩, where H is the Hamiltonian operator. The expectation value of V represents the average value of the potential energy of a quantum system and provides information about the system's dynamics and stability. However, there are limitations to using Ehrenfest's theorem, as it is only applicable to certain systems and does not take into account quantum effects.

## Homework Statement

I have a general question how I calculate the expectation value of V (potential energy) with Ehrenfest’s theorem. Do I have to integrate d<p>/dt with respect to d<x>. Also if the potential is symmetric (even) would that mean the expectation value of the potential is 0?

## The Attempt at a Solution

Can you explain your notation ? In particular "integrate ... with respect to d<x>" ?

See the reference 2 in google Ehrenfest (you did google, didn't you ?).

By the way, your post violates the PF rules/guidelines and will probably be removed ...

## What is Ehrenfest's theorem?

Ehrenfest's theorem is a mathematical theorem in quantum mechanics that relates the time evolution of a quantum system to the expectation value of its observables.

## How is Ehrenfest's theorem used to calculate the expectation value of V?

Ehrenfest's theorem states that the time derivative of the expectation value of an observable is equal to the expectation value of the commutator of that observable with the Hamiltonian operator. In the case of V, this can be written as d⟨V⟩/dt = ⟨[V, H]⟩, where H is the Hamiltonian operator. By solving this equation, the expectation value of V can be calculated.

## What is the significance of the expectation value of V?

The expectation value of V represents the average value of the potential energy of a quantum system. It is an important quantity in understanding the behavior and properties of the system.

## What does the expectation value of V tell us about the system?

The expectation value of V provides information about the average potential energy of the system. It can also give insights into the dynamics and stability of the system.

## Are there any limitations to using Ehrenfest's theorem to calculate the expectation value of V?

Yes, there are some limitations to using Ehrenfest's theorem. It is only applicable to systems with time-independent Hamiltonians and can be inaccurate for highly non-classical or highly excited states. Additionally, it does not take into account quantum effects such as tunneling and entanglement.