Energy States of Electrons in Free Space

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SUMMARY

The discussion centers on the energy states of electrons in free space, distinguishing between continuous and discontinuous states. It establishes that the energy of an electron in free space is continuous, while that near an atomic nucleus is discontinuous. The conversation introduces the concept of bound state energies corresponding to poles in the Green's function and identifies a cutoff hyperbola that separates discrete bound states from continuous free particle states. Additionally, it highlights the lack of limits on electron orbit radii around a nucleus, complicating the notions of proximity.

PREREQUISITES
  • Quantum Mechanics (QM) principles
  • Quantum Field Theory (QFT) fundamentals
  • Green's function methodology
  • Understanding of bound and free particle states
NEXT STEPS
  • Study the implications of the cutoff hyperbola in quantum systems
  • Explore the role of Green's functions in quantum mechanics
  • Investigate the differences between bound and free states in quantum field theory
  • Examine the mathematical formulation of electron orbit radii in atomic structures
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Physicists, quantum mechanics students, and researchers interested in the behavior of electrons in various energy states and their implications in atomic and particle physics.

Jackrell
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the energy of an electron in free space = the continuous state.
The energy of an electron near the nucleus of an atom = the discontinuous state.

Are there other states? Is there a theory of states.
 
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The bound state energies of systems of particles correspond to poles in the green's function. There is in general a 'cutoff hyperbola' for which below the cutoff, the energy spectrum is discrete and composed of bound states and above the cutoff there is a continuous spectrum and free particle states. There is a fundamental difference when using the equation of QM/QFT to calculate interactions of systems of particles.

In regard to the radii of electron orbits around a nucleas, there is no limit to this radius so concepts like near or far do not really make sense. The answer is not difficult to obtain but to be concise would take a while. Would you like to do this?
 

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