# Gauge Invariance in Hamiltonian

## Homework Statement

Hello Everyone
I'm wondering, why in below product rule was not used for gradient of A where exponential is treated as constant for divergent of A and only for first term of equation we used the product rule?

## Homework Equations

https://ibb.co/gHOauJ

## The Attempt at a Solution

That is, it is $(\nabla\cdot A)(e^{\lambda}\psi)$ , it is not $\nabla \cdot (Ae^{\lambda}\psi)$