Physics Monkey said:I assume we are talking 1d here? So you've solved the 1d Schrodinger equation and have obtained the bound states of the system, right? You've put your first electron into the ground state, now what is the lowest energy single particle state available to the next electron? (Hint: the electron has spin 1/2)
positron said:for a symmetrical potential with one electron, i know that the wavefunctions are symmetric or antisymmetric. for the ground state why is the wavefunction symmetric?
The ground state symmetry of a single electron with a non-interacting second electron is described by the Pauli exclusion principle, which states that no two electrons can occupy the same quantum state. This means that the two electrons must have opposite spins, resulting in a total spin of zero.
The ground state symmetry of the electrons dictates their behavior in terms of their spin and energy levels. The Pauli exclusion principle ensures that the electrons remain in their lowest possible energy state, known as the ground state, and that their spins are opposite to each other.
The ground state symmetry of the electrons is a fundamental property of quantum mechanics and cannot be changed. As long as the electrons are non-interacting, they will maintain their opposite spins and remain in their ground state.
The ground state symmetry plays a crucial role in the stability of atoms. Without the Pauli exclusion principle, electrons would be able to occupy the same quantum state, leading to unstable and unpredictable behavior. The ground state symmetry ensures that electrons are distributed in a stable manner, making atoms more stable.
There are some exceptions to the ground state symmetry of non-interacting electrons, such as in the case of superconductors. In superconductors, electrons form pairs with opposite spins, breaking the ground state symmetry. However, this is a special case and does not apply to most non-interacting electrons.