Hydrogen atom ground state with zero orbital angular moment question.

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SUMMARY

The discussion centers on the ground state of the hydrogen atom and its orbital angular momentum, specifically addressing the implications of symmetry in the wavefunction derived from the Schrödinger equation. Participants confirm that the ground state wavefunction is independent of angular variables (theta and psi), leading to an expectation value of zero for orbital angular momentum. The conversation highlights the importance of symmetry in the Coulomb potential and clarifies that while the wavefunction exhibits parity, it does not necessarily imply spherical symmetry.

PREREQUISITES
  • Understanding of the Schrödinger equation
  • Familiarity with quantum mechanics concepts such as wavefunctions and angular momentum
  • Knowledge of symmetry properties in quantum systems
  • Basic grasp of the hydrogen atom model
NEXT STEPS
  • Study the implications of symmetry in quantum mechanics
  • Explore the properties of wavefunctions in quantum systems
  • Learn about the significance of parity in quantum mechanics
  • Investigate the relationship between potential symmetry and wavefunction symmetry
USEFUL FOR

Students and professionals in physics, particularly those focusing on quantum mechanics, wavefunction analysis, and atomic structure, will benefit from this discussion.

xfshi2000
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Hi all:
As we know, if we solve the Schrödinger equation, the ground state wavefunction is independent of theta and psi. We find the expectation value of ground state orbital angular momentum is zero. But if we don't do any mathematical calculation, can we conlude that?
For example, Due to symmetry of coulomb potential, Hydrogen atom (one proton plus one electron) wavefunction must be symmetric or antisymmetric (for ground state, there is no degeneracy). Then I am stuck. How can I conclude that only by virtue of physical concept or symmetry? Does symmetry means spherical symmetry?
thanks

xf
 
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well symmetric with respect to partiy : spatial inversion. C.f with particle in box solutions.
 
malawi_glenn said:
well symmetric with respect to partiy : spatial inversion. C.f with particle in box solutions.

Thank you. What is C.f? parity property only determines psi(-x)=+/-psi(x). where x is vector. It doesn't mean it is spherical symmetry. Could you explain more? thanks
 
c.f means "compare with"

No, the wavefunctions just need to have positive or negative parity eigenvalue. I don't think there is a theorem which states that the symmetry of the ground state wave function must have the same symmetry as the potential.
 

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