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hokhani
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Can one deduce from Pauli's exclusion principle (through the Slater Determinant) that two electrons with different spins in the same energy level, can't have the same position?
It says, "No two electrons in a system can be in the same one-particle state... Note that in the statement “one-particle state” refers to both space and spin parts."Jilang said:Page 3 of the following link says so?
http://www.physics.metu.edu.tr/~sturgut/slater.pdf
hokhani said:Let me explain my problem clearly. In the expression [itex]\psi _\alpha (x)[/itex] for wave function of an electron, [itex]\alpha[/itex] is the state and [itex]x[/itex] includes both position and spin. I don't know whether [itex]\alpha[/itex] includes the spin or not and if it includes spin, is this spin the spin existed in the [itex]x[/itex]?
It works like this: In reality, there is no wave function for an electron. There is only a single wave function for the N-electron system. In the Hartree-Fock approximation, this is a single Slater determinant Θ (and in the general case, it can be written as a linear combination of Slater determinants).hokhani said:I haven't got any answer to the question above. Could anyone please answer the question?
The Pauli exclusion principle states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously. In other words, two fermions cannot have the exact same set of quantum numbers (such as position, energy, and spin) in a given system.
The Pauli exclusion principle plays a crucial role in determining the electronic structure of atoms. It allows for the formation of stable atoms by limiting the number of electrons that can occupy a given energy level. This principle also explains the stability of matter and the properties of elements in the periodic table.
The position-state restriction, also known as the Heisenberg uncertainty principle, states that the more precisely the position of a particle is known, the less precisely its momentum can be known, and vice versa. This principle is related to the Pauli exclusion principle because the two principles work together to restrict the possible quantum states that a fermion can occupy in a given system.
No, the Pauli exclusion principle is a fundamental law of quantum mechanics and has been experimentally verified numerous times. It is considered to be one of the most well-established principles in physics.
The Pauli exclusion principle explains why electrons in a solid material organize themselves into energy bands, with each band containing a maximum of two electrons with opposite spins. This behavior allows for the formation of solid materials and the diverse properties they exhibit, such as electrical conductivity and magnetism.