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In this work we investigate the $q$-deformation of the $so(4)$ dynamical symmetry of the hydrogen atom using the theory of the quantum group $su_q(2)$. We derive the energy spectrum in a physically consistent manner and find a degeneracy breaking as well as a smaller Hilbert space. We point out that using the deformed Casimir as was done before leads to inconsistencies in the physical interpretation of the theory.
We show that the relativistic hydrogen atom possesses an SO(4) symmetry by introducing a kind of pseudo-spin vector operator. The same SO(4) symmetry is still preserved in the relativistic quantum system in presence of an U(1) monopolar vector potent
The bound state energy eigenvalues for the two-dimensional Kepler problem are found to be degenerate. This accidental degeneracy is due to the existence of a two-dimensional analogue of the quantum-mechanical Runge-Lenz vector. Reformulating the prob
It is shown that hydrogen atom is a unique object in physics having negative energy of electric field, which is present in the atom. This refers also to some hydrogen-type atoms: hydrogen anti-atom, atom composed of proton and antiproton, and positronium.
We provide several examples and an intuitive diagrammatic representation demonstrating the use of two-qubit unitary transformations for mapping coupled spin Hamiltonians to simpler ones and vice versa. The corresponding dualities may be exploited to
We introduce the notion of Mixed Symmetry Quantum Phase Transition (MSQPT) as singularities in the transformation of the lowest-energy state properties of a system of identical particles inside each permutation symmetry sector $mu$, when some Hamilto