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2013

On the symmetry of the quantum-mechanical particle in a cubic box

Fernández, Francisco M.

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In this paper we show that the point-group (geometrical) symmetry is insufficient to account for the degeneracy of the energy levels of the particle in a cubic box.

The discrepancy is due to hidden (dynamical symmetry).
We obtain the operators that commute with the Hamiltonian one and connect eigenfunctions of different symmetries.
We also show that the addition of a suitable potential inside the box breaks the dynamical symmetry but preserves the geometrical one.The resulting degeneracy is that predicted by point-group symmetry.

On the symmetry of the quantum-mechanical particle in a cubic box · Around

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Tinkham M 1964 Group Theory and Quantum Mechanics
1964
Earlier work this paper cites.
Pilar F L 1968 Elementary Quantum Chemistry
1968
Earlier work this paper cites.
Shaw G B 1974 J. Phys. A
1974
Earlier work this paper cites.
Ter Haar D 1975 Problems in Quantum Mechanics
1975
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McQuarrie D A 1976 Statistical Mechanics
1976
Earlier work this paper cites.

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Then

Fernández F M 2001 Introduction to Perturbation Theory in Quantum Mechanics
2001
Later among the works it cites.
Fernández F M 2013 On the symmetry of the quantum-mechanical particle in a cubic box arXiv:1310.5136 [quant-ph]
Original
2013
Closest in time.
Hernández-Castillo A O and Lemus R 2013 J. Phys. A
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Delibas A, Aykan V, Turkkan D, and Akkus H 2013 Am. J. Mod. Phys
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