Symmetry and Degeneracy

@inproceedings{McIntosh1971SymmetryAD,
  title={Symmetry and Degeneracy},
  author={Harold V. McIntosh},
  year={1971}
}
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49 Citations
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49 Citations

Dynamical supersymmetry of the magnetic monopole and the 1/r2-potential

We examine the recently discovered dynamical OSp(1, 1) supersymmetry of the Pauli Hamiltonian for a spin 1/2 particle with gyromagnetic ratio 2, in the presence of a Dirac magnetic monopole. Using…

Does accidental degeneracy imply a symmetry group

Symmetries and conservation laws in classical and quantum mechanics

AbstractIn Part 1 of this two-part article we have spelt out, in some detail, the link between symmetries and conservation principles in the Lagrangian and Hamiltonian formulations of classical…

The 2:1 anisotropic oscillator, separation of variables and symmetry group in Bargmann space

We present a detailed analysis of the separation of variables for the time‐dependent Schrodinger equation for the anisotropic oscillator with a 2:1 frequency ratio. This reduces essentially to the…

N 93-27347 SYMMETRY ALGEBRA OF A GENERALIZED ANISOTROPIC HARMONIC OSCILLATOR

It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized…

Hidden symmetry and the number-theoretic structure of the energy levels of a perturbed harmonic oscillator

Accidental degeneracies and symmetry groups

It is usually assumed that the appearance of accidental degeneracy in the energy levels of a given Hamiltonian is due to a symmetry group. By considering the elementary problem of a rotator with…

Accidental degeneracies in the zeeman effect and the symmetry groups

Quantum superintegrability and exact solvability in n dimensions

A family of maximally superintegrable systems containing the Coulomb atom as a special case is constructed in n-dimensional Euclidean space. Two different sets of n commuting second-order operators…

Art or science: The determination of the symmetry Lie algebra for a Hamiltonian with accidental degeneracy

References

SHOWING 1-10 OF 168 REFERENCES

REMARKS ON THE RELATIVISTIC KEPLER PROBLEM

By means of a new representation, the Dirac-Coulomb spherical wave functions are treated in a manner which brings out the close formal similarity between these solutions and the spherical wave…

On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit

By a canonical transformation on the Dirac Hamiltonian for a free particle, a representation of the Dirac theory is obtained in which positive and negative energy states are separately represented by…

ROLE OF SPIN IN THE MONOPOLE PROBLEM

The scattering of an electric charge from a magnetic monopole is discussed in a way which explicitly incorporates conservation of angular momentum. The Dirac quantization condition for the physical…

Degeneracy of the Dirac Equation with Electric and Magnetic Coulomb Potentials

Investigation is made of the symmetry and degeneracy of the Dirac equation for a Coulomb potential with a fixed center bearing both electric and magnetic charge. Seen from the viewpoint of classical…

On the Degeneracy of the Two-Dimensional Harmonic Oscillator

A further study of the degeneracy of the two dimensional harmonic oscillator is made, both in the isotropic and anisotropic cases. By regarding the Hamiltonian as a linear operator acting through the…

The Symmetrical Top in the Undulatory Mechanics

BY applying the methods of Schrödinger (Ann. d. Phys., 79, 361, 489, 734, 1926), which have proved so fruitful in treating atomic problems, to the case of the symmetrical top, we have obtained a…

Degeneracy of Cyclotron Motion

The classical problem of planar cyclotron motion of a charged particle in a uniform magnetic field possesses symmetries which account for the ``accidental'' degeneracies of the analogous…

INTRINSIC MAGNETIC MOMENT AS A NONRELATIVISTIC PHENOMENON

It is shown that the Hilbert space of spin 12 particles, elementary under the Galilei group, decomposes into two subspaces invariant under the “static” Galilei group. This fact implies a…

Nonrelativistic particles and wave equations

This paper is devoted to a detailed study of nonrelativistic particles and their properties, as described by Galilei invariant wave equations, in order to obtain a precise distinction between the…

Degeneracy of the n-Dimensional, Isotropic, Harmonic Oscillator

We show that what has previously been considered the "accidental" degeneracy in the energy levels of the $n$-dimensional, isotropic, harmonic oscillator is actually a consequence of its symmetry…
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