Exchange splitting of energy levels of a system?

genericusrnme
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Exchange splitting of energy levels of a system??

Hey guys, I was just reading my QM book and came across this;

Homework Statement


Determine the exchange splitting of energy levels of a system of two electrons, regarding the interaction of the two electrons are a perturbation.

My question is, what is/are exchange splitting of energy levels of a system?

My attempt to google an answer just lead me to another empty, dead thread here on PF, I hope this thread doesn't have the same fate o:)
 
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Exchange splitting of energy levels of a system is the splitting or separation of energy levels due to the exchange interaction between two electrons. This interaction is a result of the Pauli Exclusion Principle, which states that two electrons must occupy different quantum states. In other words, this exchange splitting is caused by the repulsion of two electrons in the same orbital. As a result, the energy levels of the system become split, with one energy level being higher than the other.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!
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