Gauge Invariance in Hamiltonian

  • #1

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

 

Answers and Replies

  • #2
Delta2
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Because the divergence operator is applied only to A and then you have multiplication with exponential and psi.
That is, it is ##(\nabla\cdot A)(e^{\lambda}\psi)## , it is not ##\nabla \cdot (Ae^{\lambda}\psi)##
 
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