Why this system has a rotational symmetry in Dirac equation?

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SUMMARY

The discussion centers on the rotational symmetry inherent in the Dirac equation, particularly in its application to free electrons and hydrogen atoms. It is established that systems with constant potential, such as single or multiple electron configurations, exhibit this symmetry. However, when extending the Dirac equation to diatomic molecules, this rotational symmetry is not applicable. This distinction highlights the limitations of the Dirac equation in more complex molecular systems.

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  • Understanding of the Dirac equation and its applications
  • Familiarity with quantum mechanics concepts, particularly rotational symmetry
  • Knowledge of atomic structures, specifically hydrogen and diatomic molecules
  • Basic principles of potential energy in quantum systems
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  • Research the implications of rotational symmetry in quantum mechanics
  • Study the application of the Dirac equation in multi-electron systems
  • Explore the differences between single-electron and multi-electron quantum systems
  • Investigate advanced quantum mechanics topics related to diatomic molecules
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Physicists, quantum mechanics students, and researchers focusing on the Dirac equation and its implications in atomic and molecular systems.

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why system has a rotational symmetry in dirac equation?
is that a general property of all systems?
 
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Because Dirac equation was initially applied to free-electrons and an electron in hydrogen atom. Space of constant potential and that containing only one atom (generally multiple electron) must have rotational symmetry. If, however, you want to extend Dirac equation to diatomic molecules, rotational symmetry does not apply.
 
blue_leaf77 said:
Because Dirac equation was initially applied to free-electrons and an electron in hydrogen atom. Space of constant potential and that containing only one atom (generally multiple electron) must have rotational symmetry. If, however, you want to extend Dirac equation to diatomic molecules, rotational symmetry does not apply.
Thank you so much. it's really helpful!
 

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