The Born Interpretation

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`"probability"=|Psi(r,t)|^2deltaV=|Psi_a(r,t)+Psi_b(r,t)|^2deltaV`

`"probability"=[Psi_a(r,t)^**+Psi_b(r,t)^**][Psi_a(r,t)+Psi_b(r,t)]deltaV`

Note, `Psi(...)^**` denotes the wavefunction complex conjugate.

For the sake of clarity, we omit the wavefunction arguments, but it is understood `Psi=Psi(r,t)`

`"probability"=[Psi_a^**Psi_a+Psi_b^**Psi_a+Psi_a^**Psi_b+Psi_b^**Psi_b]deltaV`

We note that `Psi_a^**Psi_a=|Psi_a|^2`, thus,

`"probability"=[|Psi_a|^2+|Psi_b|^2+Psi_b^**Psi_a+Psi_a^**Psi_b]deltaV`

See