What is residual Coulomb interaction and why does it exist?

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SUMMARY

Residual Coulomb interaction refers to the neglected components of the Coulomb interaction in various quantum mechanical contexts, particularly in the Hartree-Fock approximation. This interaction arises from the fluctuations of charge around the nucleus, which are not accounted for in simpler models, leading to discrepancies in predicted states and angular momentum values. The discussion highlights that the term can encompass different concepts, including correlation energy and the Breit interaction, depending on the theoretical framework being applied.

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  • Understanding of Hartree-Fock approximation
  • Familiarity with many-body perturbation theory
  • Knowledge of quantum mechanics and atomic structure
  • Basic concepts of Coulomb interaction
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  • Research the Hartree-Fock approximation and its limitations
  • Explore many-body perturbation theory in quantum mechanics
  • Study correlation energy and its implications in quantum systems
  • Investigate the Breit interaction and its role in relativistic quantum mechanics
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Students and professionals in quantum mechanics, atomic physics, and theoretical chemistry seeking to deepen their understanding of Coulomb interactions and their implications in various quantum models.

Sonko
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Towards the end of my atomic and quantum course my lecturer makes a note of residual Coulomb interaction and does a few graphs to show the concequences of it are (such as some states not being allowed do to symmetry) and that they favour larger values of angular momentum, but doesn't really explain very well what it acually is and where it comes from. I was wondering if somebody could acually explain to me then what residual Coulomb interaction is and why it exists?
my first thoughts are that it may be due to the fluctuations of charge around the nucleus of an atom as the Hartree-Fock approximation ignores this and so that theory doesn't match what we see but that's the limit to my understanding.

Thanks
 
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I'm not sure what your teacher means either, since "residual coulomb interaction" could mean any neglected part of a Coulomb interaction in any context.

Without knowing the context, I can't say. If he's talking about Hartree-Fock, he could mean the neglected dynamical effects you mention, but that's usually termed the "correlation energy". If he's talking about many-body perturbation theory, then it's something else. Or he could be talking about the Breit interaction, which is the relativistic effect caused by the coulomb potential acting at a finite speed.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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