What Does Azimuthal Symmetry Mean in Physics?

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SUMMARY

Azimuthal symmetry in physics refers to a system's invariance under rotation around a specific axis, typically the z-axis. This concept is defined mathematically by the condition m=0, indicating that the system's properties remain unchanged when rotated by any angle between 0 and 2π. An example of azimuthal symmetry is found in two concentric spheres with different potentials, which exhibit spherical symmetry, a broader category that includes axial symmetry.

PREREQUISITES
  • Understanding of azimuthal symmetry in physics
  • Familiarity with spherical coordinates
  • Knowledge of potential theory
  • Basic concepts of rotational symmetry
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  • Study the mathematical formulation of azimuthal symmetry in physical systems
  • Explore the implications of spherical symmetry in electrostatics
  • Learn about the role of axial symmetry in quantum mechanics
  • Investigate applications of symmetry in conservation laws
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Students of physics, researchers in theoretical physics, and professionals working with systems exhibiting rotational symmetry will benefit from this discussion.

ahmad1992
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Anyone can explain me what is the physical meaning of azimuthal symmetry?
Based on the book, azimuthal symmetry means when m=0.
However how can we determine that a system is azimuthal symmetry or not?
Like for example, I have a two concentric spheres with radius a and b and hold at different potential.
 
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A system has azimuthal symmetry, if there exists an axis of rotation(usually called the z axis), such that if you rotate the system by an angle 0 \leq \phi \leq 2\pi around that axis, it doesn't change.
 
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ahmad1992 said:
Like for example, I have a two concentric spheres with radius a and b and hold at different potential.
That system has spherical symmetry, which includes axial symmetry.
 

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