Validity of Two-Fermion System Wavefunction with Quantum Numbers a and b

[FilipLand]

Homework Statement

Is the statement ”Given a two-fermion system, and two orbitals φ labeled by quantum numbers a, b, the two-body wavefunction (1,2 represent the particle variables)

$$\psi(1,2) = \phi_a(1) \phi_a(2) - \phi_b(1) \phi_b(2) + \phi_a(1) \phi_b(2) - \phi_b(1) \phi_a(2) $$

correctly describes a possible state of the system” true or false ? Explain your answer

Homework Equations

I think this should be done by arguing so so relevant equations.

The Attempt at a Solution

There's a few of these problems with different wave functions. I'm not sure how to approach these problems.

Maybe by noticing that input (1,2) as not consistent to $\phi_a$ and $\phi_b$, respectively and can hence not describe a quantum state?

 

[blue_leaf77]

The wavefunction of a fermionic system must be antisymmetric in the interchange of fermions, in your case the wavefunction should satisfy
$$
\psi(1,2) = -\psi(2,1).
$$
You just need to check whether the above relation is satisfied.

 

[FilipLand]

Thank you!