# Is it possible to find an operator on wavefunctions that results in nonconservative forces?

The Schrodinger equation for a particle in a potential is,

$$i\hbar \partial_t \varphi = \left( \frac{p^2}{2m} + V(x) \right) \varphi$$

where p is the momentum operator and $V$ is the potential. This gives dynamics that approximately follow Newton's laws,

$$m \frac{d}{dt}\left<x\right>=\left<p\right>\\\frac{d}{dt}\left<p\right>=-\left<V'(x)\right>$$

Is there an operator you can add to the Schrodinger equation to account for nonconservative forces such that

$$m \frac{d}{dt}\left<x\right>=\left<p\right>\\\frac{d}{dt}\left<p\right>=-\left<V'(x)\right> + \left< F_{nc}(x,p) \right>$$

This question was asked previously as part of another post but separated into this new one. Here's the other post:

Why is a bath necessary for nonconservative forces in quantum mechanics

• What about a potential with explicit time-dependence? – probably_someone Mar 30 '18 at 1:13
• Possibly. Do you know how to get a time dependent potential that gives the dynamics above? – Ravi Mar 30 '18 at 1:22