Exploring Azimuthal Symmetry: What is its Physical Meaning?

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In summary, azimuthal symmetry refers to when m=0 according to the book. To determine if a system has azimuthal symmetry, there must be an axis of rotation (typically the z axis) where rotating the system around that axis by an angle 0 \leq \phi \leq 2\pi does not change the system. For example, a system with two concentric spheres of different radii and held at different potentials has spherical symmetry, which includes axial symmetry.
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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 [itex] 0 \leq \phi \leq 2\pi [/itex] 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.
 

FAQ: Exploring Azimuthal Symmetry: What is its Physical Meaning?

1. What is azimuthal symmetry?

Azimuthal symmetry is a type of rotational symmetry where an object appears the same when rotated around a specific axis or point. In other words, the object has the same shape and properties at every angle of rotation.

2. What is the physical significance of azimuthal symmetry?

Azimuthal symmetry has physical significance in many areas of science, including physics, chemistry, and biology. It is often observed in natural phenomena, such as the formation of crystals, the structure of molecules, and the arrangement of planets in our solar system.

3. How is azimuthal symmetry related to the laws of physics?

Azimuthal symmetry is related to the laws of physics in that it reflects the underlying principles of symmetry and conservation of energy. In physics, the laws of conservation state that certain properties, such as mass, energy, and momentum, remain constant in a closed system. Azimuthal symmetry is a manifestation of these laws in systems that exhibit rotational symmetry.

4. Can azimuthal symmetry be broken?

Yes, azimuthal symmetry can be broken in certain circumstances. This can occur due to external forces acting on the system or inherent imperfections in the system. For example, a perfectly spherical object may lose its azimuthal symmetry if it is subjected to external forces that cause it to deform.

5. How is azimuthal symmetry used in scientific research?

Azimuthal symmetry is used in scientific research to study and understand various phenomena in nature. It is also a fundamental concept in many scientific theories, such as quantum mechanics and relativity. Scientists use azimuthal symmetry as a tool to simplify complex systems and make predictions about their behavior and properties.

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