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Lola1

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In summary, the energy spectrum of a particle constrained to move on the edge of a circumference is continuous and two times degenerate due to the fact that it can move in both clockwise and counterclockwise directions. This degeneracy is indicated by the 2 in the exponent of the exponential solution, but it does not affect the spacing of the energy levels. The difference between energy levels is determined by the potential, while the multiplicity is based on the symmetry.

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Lola1

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mfb

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Lola1

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ψ (x) = α \exp (2i (nπ / L ) x) + β \exp (-2i (nπ / L) x)

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mfb

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I don't understand that sentence.Lola1 said:Mathematically double degeneration is known by 2 that multiplies the exponents of the exponential solution?

You can write down the general solution like that, but you can also let n be positive or negative, and of course you can always have superpositions of those solutions.

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Lola1

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mfb

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The difference between energy levels is independent of the multiplicities. It arises from the detailed structure of the potential, while the multiplicity is based on the symmetry. Every symmetric potential will have this multiplicity, but it can have different steps between the energy levels.

Spectrum energy refers to the range of energies that a particle can have while moving on a circumference. It is determined by the particle's velocity and the circumference of the circle it is moving on.

The spectrum energy of a particle is directly related to its movement on a circumference. As the particle's speed and/or the circumference of the circle increases, the spectrum energy also increases.

Understanding spectrum energy is important for studying and predicting the behavior of particles moving on a circumference. It can help us understand how these particles interact with their surroundings and how their energy levels change over time.

Spectrum energy is calculated using the formula E = (1/2)mv^2, where E is the energy, m is the mass of the particle, and v is its velocity.

The spectrum energy of a particle can be affected by its mass, velocity, and the circumference of the circle it is moving on. Other factors such as external forces, friction, and collisions may also play a role in changing the particle's energy levels.

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