Is the Classical Electric Potential a Valid Approximation in Quantum Mechanics?

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SUMMARY

The discussion confirms that using the classical electric potential in the Schrödinger equation for the hydrogen atom is a very good approximation. However, it highlights the need for more accurate frameworks, such as Quantum Electrodynamics (QED), which quantizes the electromagnetic potential. Additionally, relativistic corrections can be addressed through the Dirac Equation, providing a more comprehensive understanding of the interactions at play.

PREREQUISITES
  • Understanding of the Schrödinger equation
  • Familiarity with classical electric potential
  • Knowledge of Quantum Electrodynamics (QED)
  • Basic concepts of relativistic physics and the Dirac Equation
NEXT STEPS
  • Research Quantum Electrodynamics (QED) and its implications for electromagnetic potentials
  • Study the Dirac Equation and its role in relativistic quantum mechanics
  • Explore the concept of Second Quantization in quantum field theory
  • Investigate the limitations of classical approximations in quantum mechanics
USEFUL FOR

Physicists, quantum mechanics students, and researchers interested in the intersection of classical and quantum theories, particularly in the context of atomic physics and electromagnetic interactions.

cragar
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When we setup the Schrödinger equation for the hydrogen atom we use the classical electric potential. It seems that we would need a new potential instead of mixing QM and classical.
Is this just a very good approximation or is there something subtle.
 
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cragar said:
When we setup the Schrödinger equation for the hydrogen atom we use the classical electric potential. It seems that we would need a new potential instead of mixing QM and classical.
Is this just a very good approximation or is there something subtle.

It's a very good approximation. For one, relativistic corrections exist (but that's not what you're asking) that come about with the Dirac Equation. As for your question, in what is termed "Second Quantization", the electromagnetic potential can also be quantized. This is the field of Quantum Electrodynamics (QED). It provides the most accurate framework for including the electromagnetic potentials.
 
thanks for your answer. if its not to much trouble how do they correct for relativity in the potential.
 

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