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\begin{align}
& i\hbar \frac{\partial }{\partial t}{{\left| \Psi (\bar{r},t) \right|}^{2}}=\frac{-{{\hbar }^{2}}}{2m}\left( \Psi *\Delta \Psi -\Psi \Delta \Psi * \right)+\frac{{{e}^{2}}}{2m}\left[ \Psi *{{{\bar{A}}}^{2}}\Psi -\Psi {{{\bar{A}}}^{2}}\Psi * \right]+\Psi *V\Psi -\Psi V\Psi * \\
& \quad \quad \quad \quad \quad \quad +\frac{i\hbar e}{2m}\left( \Psi *\nabla \left( \bar{A}\Psi  \right)+\bar{A}\Psi \nabla \Psi *+\Psi \nabla \left( \bar{A}\Psi * \right)+\bar{A}\Psi *\nabla \Psi  \right) \\
& \Psi *{{{\bar{A}}}^{2}}\Psi -\Psi {{{\bar{A}}}^{2}}\Psi *=0 \\
& \Psi *V\Psi -\Psi V\Psi *=0 \\
& \Psi *\nabla \left( \bar{A}\Psi  \right)+\bar{A}\Psi \nabla \Psi *=\Psi \nabla \left( \bar{A}\Psi * \right)+\bar{A}\Psi *\nabla \Psi =\nabla \left( \Psi \bar{A}\Psi * \right) \\
& \Rightarrow i\hbar \frac{\partial }{\partial t}{{\left| \Psi (\bar{r},t) \right|}^{2}}=\frac{-{{\hbar }^{2}}}{2m}\left( \Psi *\Delta \Psi -\Psi \Delta \Psi * \right)+\frac{i\hbar e}{m}\nabla \left( \Psi \bar{A}\Psi * \right) \\
& \Psi *\Delta \Psi -\Psi \Delta \Psi *=\nabla \left( \Psi *\nabla \Psi -\Psi \nabla \Psi * \right)-\left( \nabla \Psi *\nabla \Psi -\nabla \Psi \nabla \Psi * \right) \\
& \left( \nabla \Psi *\nabla \Psi -\nabla \Psi \nabla \Psi * \right)=0 \\
& \Rightarrow i\hbar \frac{\partial }{\partial t}{{\left| \Psi (\bar{r},t) \right|}^{2}}=\frac{-{{\hbar }^{2}}}{2m}\nabla \left( \Psi *\nabla \Psi -\Psi \nabla \Psi * \right)+\frac{i\hbar e}{m}\nabla \left( \Psi \bar{A}\Psi * \right) \\
& \Rightarrow i\hbar \frac{\partial }{\partial t}{{\left| \Psi (\bar{r},t) \right|}^{2}}=\nabla \left[ \frac{-{{\hbar }^{2}}}{2m}\left( \Psi *\nabla \Psi -\Psi \nabla \Psi * \right)+\frac{i\hbar e}{m}\left( \Psi \bar{A}\Psi * \right) \right] \\
\end{align}

TeX (checked): 

{\begin{aligned}&i\hbar {\frac {\partial }{\partial t}}{{\left|\Psi ({\bar {r}},t)\right|}^{2}}={\frac {-{{\hbar }^{2}}}{2m}}\left(\Psi *\Delta \Psi -\Psi \Delta \Psi *\right)+{\frac {{e}^{2}}{2m}}\left[\Psi *{{\bar {A}}^{2}}\Psi -\Psi {{\bar {A}}^{2}}\Psi *\right]+\Psi *V\Psi -\Psi V\Psi *\\&\quad \quad \quad \quad \quad \quad +{\frac {i\hbar e}{2m}}\left(\Psi *\nabla \left({\bar {A}}\Psi \right)+{\bar {A}}\Psi \nabla \Psi *+\Psi \nabla \left({\bar {A}}\Psi *\right)+{\bar {A}}\Psi *\nabla \Psi \right)\\&\Psi *{{\bar {A}}^{2}}\Psi -\Psi {{\bar {A}}^{2}}\Psi *=0\\&\Psi *V\Psi -\Psi V\Psi *=0\\&\Psi *\nabla \left({\bar {A}}\Psi \right)+{\bar {A}}\Psi \nabla \Psi *=\Psi \nabla \left({\bar {A}}\Psi *\right)+{\bar {A}}\Psi *\nabla \Psi =\nabla \left(\Psi {\bar {A}}\Psi *\right)\\&\Rightarrow i\hbar {\frac {\partial }{\partial t}}{{\left|\Psi ({\bar {r}},t)\right|}^{2}}={\frac {-{{\hbar }^{2}}}{2m}}\left(\Psi *\Delta \Psi -\Psi \Delta \Psi *\right)+{\frac {i\hbar e}{m}}\nabla \left(\Psi {\bar {A}}\Psi *\right)\\&\Psi *\Delta \Psi -\Psi \Delta \Psi *=\nabla \left(\Psi *\nabla \Psi -\Psi \nabla \Psi *\right)-\left(\nabla \Psi *\nabla \Psi -\nabla \Psi \nabla \Psi *\right)\\&\left(\nabla \Psi *\nabla \Psi -\nabla \Psi \nabla \Psi *\right)=0\\&\Rightarrow i\hbar {\frac {\partial }{\partial t}}{{\left|\Psi ({\bar {r}},t)\right|}^{2}}={\frac {-{{\hbar }^{2}}}{2m}}\nabla \left(\Psi *\nabla \Psi -\Psi \nabla \Psi *\right)+{\frac {i\hbar e}{m}}\nabla \left(\Psi {\bar {A}}\Psi *\right)\\&\Rightarrow i\hbar {\frac {\partial }{\partial t}}{{\left|\Psi ({\bar {r}},t)\right|}^{2}}=\nabla \left[{\frac {-{{\hbar }^{2}}}{2m}}\left(\Psi *\nabla \Psi -\Psi \nabla \Psi *\right)+{\frac {i\hbar e}{m}}\left(\Psi {\bar {A}}\Psi *\right)\right]\\\end{aligned}}

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i ℏ ∂ ∂ ⁡ t | Ψ ( r ¯ , t ) | 2 = - ℏ 2 2 ⁢ m ( Ψ * Δ Ψ - Ψ Δ Ψ * ) + e 2 2 ⁢ m [ Ψ * A ¯ 2 Ψ - Ψ A ¯ 2 Ψ * ] + Ψ * V Ψ - Ψ V Ψ * + i ⁢ ℏ ⁢ e 2 ⁢ m ( Ψ * ∇ ( A ¯ Ψ ) + A ¯ Ψ ∇ Ψ * + Ψ ∇ ( A ¯ Ψ * ) + A ¯ Ψ * ∇ Ψ ) Ψ * A ¯ 2 Ψ - Ψ A ¯ 2 Ψ * = 0 Ψ * V Ψ - Ψ V Ψ * = 0 Ψ * ∇ ( A ¯ Ψ ) + A ¯ Ψ ∇ Ψ * = Ψ ∇ ( A ¯ Ψ * ) + A ¯ Ψ * ∇ Ψ = ∇ ( Ψ A ¯ Ψ * ) ⇒ i ℏ ∂ ∂ ⁡ t | Ψ ( r ¯ , t ) | 2 = - ℏ 2 2 ⁢ m ( Ψ * Δ Ψ - Ψ Δ Ψ * ) + i ⁢ ℏ ⁢ e m ∇ ( Ψ A ¯ Ψ * ) Ψ * Δ Ψ - Ψ Δ Ψ * = ∇ ( Ψ * ∇ Ψ - Ψ ∇ Ψ * ) - ( ∇ Ψ * ∇ Ψ - ∇ Ψ ∇ Ψ * ) ( ∇ Ψ * ∇ Ψ - ∇ Ψ ∇ Ψ * ) = 0 ⇒ i ℏ ∂ ∂ ⁡ t | Ψ ( r ¯ , t ) | 2 = - ℏ 2 2 ⁢ m ∇ ( Ψ * ∇ Ψ - Ψ ∇ Ψ * ) + i ⁢ ℏ ⁢ e m ∇ ( Ψ A ¯ Ψ * ) ⇒ i ℏ ∂ ∂ ⁡ t | Ψ ( r ¯ , t ) | 2 = ∇ [ - ℏ 2 2 ⁢ m ( Ψ * ∇ Ψ - Ψ ∇ Ψ * ) + i ⁢ ℏ ⁢ e m ( Ψ A ¯ Ψ * ) ] missing-subexpression fragments i Planck-constant-over-2-pi 𝑡 | Ψ fragments ( ¯ 𝑟 , t ) superscript | 2 superscript Planck-constant-over-2-pi 2 2 𝑚 fragments ( Ψ Δ Ψ Ψ Δ Ψ ) superscript 𝑒 2 2 𝑚 fragments [ Ψ superscript ¯ 𝐴 2 Ψ Ψ superscript ¯ 𝐴 2 Ψ ] Ψ V Ψ Ψ V Ψ missing-subexpression fragments 𝑖 Planck-constant-over-2-pi 𝑒 2 𝑚 fragments ( Ψ ∇ fragments ( ¯ 𝐴 Ψ ) ¯ 𝐴 Ψ ∇ Ψ Ψ ∇ fragments ( ¯ 𝐴 Ψ ) ¯ 𝐴 Ψ ∇ Ψ ) missing-subexpression fragments Ψ superscript ¯ 𝐴 2 Ψ Ψ superscript ¯ 𝐴 2 Ψ 0 missing-subexpression fragments Ψ V Ψ Ψ V Ψ 0 missing-subexpression fragments Ψ ∇ fragments ( ¯ 𝐴 Ψ ) ¯ 𝐴 Ψ ∇ Ψ Ψ ∇ fragments ( ¯ 𝐴 Ψ ) ¯ 𝐴 Ψ ∇ Ψ ∇ fragments ( Ψ ¯ 𝐴 Ψ ) missing-subexpression fragments ⇒ i Planck-constant-over-2-pi 𝑡 | Ψ fragments ( ¯ 𝑟 , t ) superscript | 2 superscript Planck-constant-over-2-pi 2 2 𝑚 fragments ( Ψ Δ Ψ Ψ Δ Ψ ) 𝑖 Planck-constant-over-2-pi 𝑒 𝑚 ∇ fragments ( Ψ ¯ 𝐴 Ψ ) missing-subexpression fragments Ψ Δ Ψ Ψ Δ Ψ ∇ fragments ( Ψ ∇ Ψ Ψ ∇ Ψ ) fragments ( ∇ Ψ ∇ Ψ ∇ Ψ ∇ Ψ ) missing-subexpression fragments fragments ( ∇ Ψ ∇ Ψ ∇ Ψ ∇ Ψ ) 0 missing-subexpression fragments ⇒ i Planck-constant-over-2-pi 𝑡 | Ψ fragments ( ¯ 𝑟 , t ) superscript | 2 superscript Planck-constant-over-2-pi 2 2 𝑚 ∇ fragments ( Ψ ∇ Ψ Ψ ∇ Ψ ) 𝑖 Planck-constant-over-2-pi 𝑒 𝑚 ∇ fragments ( Ψ ¯ 𝐴 Ψ ) missing-subexpression fragments ⇒ i Planck-constant-over-2-pi 𝑡 | Ψ fragments ( ¯ 𝑟 , t ) superscript | 2 ∇ fragments [ superscript Planck-constant-over-2-pi 2 2 𝑚 fragments ( Ψ ∇ Ψ Ψ ∇ Ψ ) 𝑖 Planck-constant-over-2-pi 𝑒 𝑚 fragments ( Ψ ¯ 𝐴 Ψ ) ] {\displaystyle{\displaystyle\begin{aligned} &\displaystyle i\hbar\frac{% \partial}{\partial t}{{\left|\Psi(\bar{r},t)\right|}^{2}}=\frac{-{{\hbar}^{2}}% }{2m}\left(\Psi*\Delta\Psi-\Psi\Delta\Psi*\right)+\frac{{{e}^{2}}}{2m}\left[% \Psi*{{{\bar{A}}}^{2}}\Psi-\Psi{{{\bar{A}}}^{2}}\Psi*\right]+\Psi*V\Psi-\Psi V% \Psi*\\ &\displaystyle\quad\quad\quad\quad\quad\quad+\frac{i\hbar e}{2m}\left(\Psi*% \nabla\left(\bar{A}\Psi\right)+\bar{A}\Psi\nabla\Psi*+\Psi\nabla\left(\bar{A}% \Psi*\right)+\bar{A}\Psi*\nabla\Psi\right)\\ &\displaystyle\Psi*{{{\bar{A}}}^{2}}\Psi-\Psi{{{\bar{A}}}^{2}}\Psi*=0\\ &\displaystyle\Psi*V\Psi-\Psi V\Psi*=0\\ &\displaystyle\Psi*\nabla\left(\bar{A}\Psi\right)+\bar{A}\Psi\nabla\Psi*=\Psi% \nabla\left(\bar{A}\Psi*\right)+\bar{A}\Psi*\nabla\Psi=\nabla\left(\Psi\bar{A}% \Psi*\right)\\ &\displaystyle\Rightarrow i\hbar\frac{\partial}{\partial t}{{\left|\Psi(\bar{r% },t)\right|}^{2}}=\frac{-{{\hbar}^{2}}}{2m}\left(\Psi*\Delta\Psi-\Psi\Delta% \Psi*\right)+\frac{i\hbar e}{m}\nabla\left(\Psi\bar{A}\Psi*\right)\\ &\displaystyle\Psi*\Delta\Psi-\Psi\Delta\Psi*=\nabla\left(\Psi*\nabla\Psi-\Psi% \nabla\Psi*\right)-\left(\nabla\Psi*\nabla\Psi-\nabla\Psi\nabla\Psi*\right)\\ &\displaystyle\left(\nabla\Psi*\nabla\Psi-\nabla\Psi\nabla\Psi*\right)=0\\ &\displaystyle\Rightarrow i\hbar\frac{\partial}{\partial t}{{\left|\Psi(\bar{r% },t)\right|}^{2}}=\frac{-{{\hbar}^{2}}}{2m}\nabla\left(\Psi*\nabla\Psi-\Psi% \nabla\Psi*\right)+\frac{i\hbar e}{m}\nabla\left(\Psi\bar{A}\Psi*\right)\\ &\displaystyle\Rightarrow i\hbar\frac{\partial}{\partial t}{{\left|\Psi(\bar{r% },t)\right|}^{2}}=\nabla\left[\frac{-{{\hbar}^{2}}}{2m}\left(\Psi*\nabla\Psi-% \Psi\nabla\Psi*\right)+\frac{i\hbar e}{m}\left(\Psi\bar{A}\Psi*\right)\right]% \\ \end{aligned}}}

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iℏ∂∂t|Ψ(r¯,t)|2=−ℏ22m(Ψ*ΔΨ−ΨΔΨ*)+e22m[Ψ*A¯2Ψ−ΨA¯2Ψ*]+Ψ*VΨ−ΨVΨ*+iℏe2m(Ψ*∇(A¯Ψ)+A¯Ψ∇Ψ*+Ψ∇(A¯Ψ*)+A¯Ψ*∇Ψ)Ψ*A¯2Ψ−ΨA¯2Ψ*=0Ψ*VΨ−ΨVΨ*=0Ψ*∇(A¯Ψ)+A¯Ψ∇Ψ*=Ψ∇(A¯Ψ*)+A¯Ψ*∇Ψ=∇(ΨA¯Ψ*)⇒iℏ∂∂t|Ψ(r¯,t)|2=−ℏ22m(Ψ*ΔΨ−ΨΔΨ*)+iℏem∇(ΨA¯Ψ*)Ψ*ΔΨ−ΨΔΨ*=∇(Ψ*∇Ψ−Ψ∇Ψ*)−(∇Ψ*∇Ψ−∇Ψ∇Ψ*)(∇Ψ*∇Ψ−∇Ψ∇Ψ*)=0⇒iℏ∂∂t|Ψ(r¯,t)|2=−ℏ22m∇(Ψ*∇Ψ−Ψ∇Ψ*)+iℏem∇(ΨA¯Ψ*)⇒iℏ∂∂t|Ψ(r¯,t)|2=∇[−ℏ22m(Ψ*∇Ψ−Ψ∇Ψ*)+iℏem(ΨA¯Ψ*)]

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