Of more formal properties of Eq. (84), it is easy to prove that its solutions satisfy the same continuity equation (1.52), with the probability current density \(\mathbf{j}\) still given by Eq. (1.47)...Of more formal properties of Eq. (84), it is easy to prove that its solutions satisfy the same continuity equation (1.52), with the probability current density \(\mathbf{j}\) still given by Eq. (1.47), but a different expression for the probability density \(w\) - which becomes very similar to that for \(\mathbf{j}\) : \[w=\frac{i \hbar}{2 m c^{2}}\left(\Psi^{*} \frac{\partial \Psi}{\partial t}-\text { c.c. }\right), \quad \mathbf{j}=\frac{i \hbar}{2 m}\left(\Psi \nabla \Psi^{*}-\text { c.c. }\…
