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Quantum Tunneling

density ρand the velocity charge velocity ~v according to J~= ρ~v.Its natural to relate the current density ρwith the electron charge eand the quantum PDF(x) according to ρ = eΨ∗(x)Ψ(x).It is equally natural to describe the velocity by ˆp/mwhere (in 3 dimensions) ˇp= −i¯h(∂/∂x) →−i¯h∇~.Of course ∇~ is an operator which needs to operate on part of ρ.

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