What is the electric field around a quantum particle?

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SUMMARY

The discussion centers on the complexities of understanding the electric field surrounding quantum particles, particularly in the context of solving the Schrödinger Equation (SE) for systems like the hydrogen atom. It highlights the necessity of considering multi-particle states due to the wavefunction of the orbiting particle, which complicates the representation of the electric field. The participant expresses confusion about whether the electric field at a point in space can be treated as a quantum observable, influenced by the probabilistic nature of particle positions. Key references include quantum electrodynamics and perturbation theory applied to multi-particle systems.

PREREQUISITES
  • Understanding of the Schrödinger Equation (SE)
  • Familiarity with quantum electrodynamics
  • Knowledge of multi-particle quantum states
  • Basic concepts of perturbation theory
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  • Study the implications of quantum electrodynamics on electric fields
  • Explore multi-particle quantum state representations
  • Learn about the role of perturbation theory in quantum mechanics
  • Investigate the concept of quantum observables in electric fields
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Students and enthusiasts of quantum mechanics, physicists exploring quantum field theory, and researchers interested in the behavior of electric fields in quantum systems.

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Beginning another attempt in my amateurish efforts to understand quantum mechanics, I suddenly realized there was a basic issue I find completely unclear.

When we solve the SE for an interesting system we first need to input a potential, which is usually some function of the spatial coordinates. For example courses often start by looking at a particle in a box, and then of course the hydrogen atom. But when we solve the hydrogen atom as a single particle state in a fixed Coloumb potential this must just be an approximation. Since in fact the thing it's orbiting must also be represented by a wavefunction. So in fact we need a multi-particle state. Now I know we must be able to deal with multi-particle states since I have vague memories knocking around of doing the helium atom using perturbation theory, but I'm having some conceptual trouble getting my head around the nature of the electric field around things that don't have a definite position. Is the E-field at some point in space also a quantum observable with some probability of being this or this, depending on the different weighting of all the combinations of possible positions of all charged particles?
 
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