Position representation of the state of the system

In summary, the conversation discusses the use of inner products between a state and eigenstates of different operators in quantum mechanics. The resulting wave function can depend on different variables, such as position, momentum, and energy. It is noted that not all operators commute with each other, and therefore, the resulting wave function may not be a simultaneous eigenstate of all operators involved. The conversation also touches on the notation for eigenstates and the use of spherical harmonics.
  • #71
Ok, thanks that is progress.

What about two independent fermions having a total antisymmetric wavefunction $$\Psi(x_1, x_2)=\psi_{a}(x_1) \psi_{b}(x_2)-\psi_a(x_2) \psi_b(x_1)$$?
This is the sum of two products not a single product but it does not mean entanglement, correct? Why not?
 

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