Nonrelativistic, without external field: {\ displaystyle \ mathbf {j} = {\ frac {-i \ hbar} {2m}} \ left (\ Psi ^ {} \ nabla \ Psi - \ Psi \ nabla \ Psi ^ {} \ right)} \ mathbf {j} = \ frac {-i \ hbar} {2m} \ left (\ Psi ^ * \ nabla \ Psi - \ Psi \ nabla \ Psi ^ \ right) {\ displaystyle = {\ frac {\ hbar} {m}} \ mathrm {Im} (\ Psi ^ {} \ nabla \ Psi) = \ mathrm {Re} (\ Psi ^ {} {\ frac {\ hbar} {im}} \ nabla \ Psi)} = \ frac \ hbar m \ mathrm {Im} (\ Psi ^ \ nabla \ Psi) = \ mathrm {Re} (\ Psi ^ * \ frac {\ hbar} {im} \ nabla \ Psi)
star * is complex conjugate
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