How can I find $\mathbf{J}$ from the following equation $$ \nabla \cdot \mathbf{J}= ∇\left(∇^2 (∇ψ^†⋅\mathbf{A})+∇⋅(\mathbf{A} ∇^2 ψ^† )\right)⋅∇ψ+∇ψ^†⋅∇\left(∇^2 (∇ψ⋅\mathbf{A} )+∇⋅(\mathbf{A} ∇^2 ψ)\right)+\left[∇^2(∇^2 ψ^† )∇ψ+∇ψ^† ∇^2 (∇^2 ψ)-∇^2 ψ^† ∇(∇^2 ψ)-∇(∇^2 ψ^† ) ∇^2 ψ\right]⋅\mathbf{A} $$ $\psi\equiv\psi(\mathbf r)$ and $\psi^†\equiv\psi^†(\mathbf r)$ are scalar field operators. And $\mathbf{A}\equiv\mathbf{A}(\mathbf r)$ is a vector field.
2026-03-27 17:23:47.1774632227
How can I find $\mathbf{J}$ from the equation for $\nabla\cdot\mathbf{J}$?
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