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winding bird
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why system has a rotational symmetry in dirac equation?
is that a general property of all systems?
is that a general property of all systems?
Thank you so much. it's really helpful!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.
Rotational symmetry in the Dirac equation refers to the property of the equation that allows for solutions to be rotated around a fixed point without changing the overall shape or form of the equation. This means that the equations describing the system remain the same regardless of the orientation of the system in space.
Rotational symmetry is important in the Dirac equation because it allows for the conservation of angular momentum, a fundamental physical quantity in quantum mechanics. This symmetry also simplifies the mathematical calculations and makes it easier to find solutions to the equation.
The rotational symmetry in the Dirac equation results in solutions that have a specific angular momentum value, known as the spin. This spin value is a fundamental property of particles and is related to rotational symmetry through the equation's solutions.
No, rotational symmetry is not present in all systems described by the Dirac equation. It is only present in systems that have a certain type of symmetry, known as spherical symmetry. This means that the system is symmetrical in all directions, like a sphere, and allows for rotation without changing the system's properties.
The implications of rotational symmetry for particles described by the Dirac equation are that their behavior is predictable and can be described by specific mathematical equations. This symmetry also allows for the conservation of angular momentum, which is crucial for understanding the behavior of particles in quantum mechanics.