I understand how to calculate the determinant. But how to construct determinant for electrons spin in an atom?atyy said:For quantum mechanics, you can think of it as the determinant as just notation and not otherwise meaningful
fricke said:I understand how to calculate the determinant. But how to construct determinant for electrons spin in an atom?
thank you!atyy said:http://jila.colorado.edu/Chem4541/Indistinguishable%20particles,%20Pauli%20Principle,%20Slater%20determinants%20p%2091-98.pdf
fricke said:Prof taught us one row represents one electron, so each electron is represented in a row in Slater Determinant. But when I googled it, some represents one electron in one column (not in one row!). Mathematically, it seems to be not wrong (since I didn't do any calculation to prove these two are the same) but how can representing electrons in column rather than row be the same in quantum electron spin?
thank you. I have found out a really easy way to construct Slater determinant for electron spin of an atom :Datyy said:I'm not entirely sure of this part, but I believe it is because the determinant is the same whether rows and columns are transposed.
https://www.khanacademy.org/math/li...-determinant-of-transpose?_escaped_fragment_=
But you should check the wave function is the same whether you write each electron as a row or a column.
A Slater determinant is a mathematical expression used to describe the quantum state of a multi-electron system, such as an atom or molecule. It is a combination of single-electron wavefunctions, known as orbitals, that takes into account the antisymmetric nature of quantum particles.
The He 1s2 orbital is represented by the product of two single-electron wavefunctions, one for each electron. These wavefunctions are typically denoted as ψ1s(x1, y1, z1) and ψ1s(x2, y2, z2), where x, y, and z represent the coordinates of each electron.
The 1s12s1 Slater determinant includes an additional orbital, the 1s orbital for the second electron. This means that the wavefunction for the second electron, ψ1s(x2, y2, z2), is now included in the determinant, resulting in a more accurate description of the system's quantum state.
Slater determinants provide a way to describe the quantum state of a multi-electron system, such as an atom, by taking into account the antisymmetric nature of quantum particles. This allows us to understand the arrangement and energy levels of electrons in an atom, which is crucial for understanding the chemical and physical properties of elements.
No, there are other methods for describing multi-electron systems, such as Hartree-Fock theory and configuration interaction. However, Slater determinants are a commonly used and effective method for understanding and describing the electronic structure of atoms and molecules.