What Is the Self-Energy of an Electron?

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Self-energy refers to the energy a point charge possesses when isolated from other charges, requiring work to assemble it from infinitesimal pieces. While the charge of an electron is the smallest unit, its self-energy is considered infinite due to the nature of point charges in quantum mechanics. This concept is crucial for understanding electron behavior in atomic and molecular systems. The idea of self-energy was first introduced by Arnold Sommerfeld in 1923 to address the anomalous Zeeman effect. Understanding self-energy is essential for deeper insights into particle interactions and quantum mechanics.
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What is so called SELF ENERGY? I know the explanation that it is the energy that a point charge has when it is by itself,at a large distance from other charges. In textbook (ohanian) says that it takes work to assemble the point charge out of infinitesimal pieces of charge.The energy needed to assemble the point charge is called the self-energy of the point charge.I know that this explanation is clear enough.But as i know e=1.6*10^-19 C , the charge of electron or proton is the smallest charge, and all other charges are INTEGER*e.So I thought that I can assume that self energy of an electron is zero.But I learned that it turns out to be Infinite...
 
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Self Energy is a concept in quantum mechanics that describes the energy of a system due to its interaction with itself. It is a form of self-inductance and is especially important in understanding the behavior of electrons in atoms and molecules.

The self-energy of an electron was first introduced in 1923 by Arnold Sommerfeld to solve the problem of the anomalous Zeeman effect.
 
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