| Slater Determinant |
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| quantum mechanics | |
| determinants | |
| pauli exclusion principle | |
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The Slater determinant arises from the consideration of a wavefunction for a collection of electrons. The wavefunction for each individual electron is known as a Spin-orbital , , where indicates the position and spin of the electron. TWO-PARTICLE CASE The simplest way to approximate the wavefunction of a many-particle system is to take the product of properly chosen ''one-electron wavefunctions'' of the individual particles. For the two-particle case, we have : This expression occurs in Hartree Theory and is known as a Hartree Product . However, it is not satisfactory for Fermions , such as electrons, because the wavefunction is not antisymmetric. An antisymmetric wavefunction can be mathematically described as follows: : Therefore the Hartree product does not satisfy the Pauli principle. This problem can be overcome by taking a linear combination of both Hartree products : where the coefficient is a Normalization Factor . This wavefunction is antisymmetric and no longer distinguishes between electrons. Moreover, it also goes to zero if any two wavefunctions or two electrons are the same. This is equivalent to satisfying the Pauli Exclusion Principle . GENERALIZATION TO THE SLATER DETERMINANT The expression can be generalised to any number of fermions by writing it as a Determinant . For an N-electron system, the Slater determinant is defined as : |
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