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How is a Slater determinant used in physics?

A Slater determinant is a representation of a many-particle wave function for a system of fermions, which satisfies the anti-symmetry requirement. In other words, that the wave function changes sign on interchange of two particle coordinates (e.g. , letting spin be regarded as another coordinate for the sake of brevity)

Which is Slater determinant for an electronic wavefunction?

Slater Determinants An electronic wavefunction for particles must be a function of coordinates: for each electron, we have , , and Cartesian coordinates plus a spin coordinate (sometimes designated , which can have values and ).

When does a Slater determinant change sign?

A Slater determinant is anti-symmetric upon exchange of any two electrons. We recall that if we take a matrix and interchange two its rows, the determinant changes sign. The wavefunctions in - can be expressed in term of the four determinants in Equations -.

Is the Slater determinant satisfactory for fermions?

However, it is not satisfactory for fermions because the wave function above is not antisymmetric under exchange of any two of the fermions, as it must be according to the Pauli exclusion principle. An antisymmetric wave function can be mathematically described as follows:

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