Abstract
The q-deformed three-dimensional harmonic oscillator is defined in terms of the q-bosons corresponding to the spherical components of a nondeformed three-dimensional oscillator. It is shown that the dynamical algebra is spq(6,R). Two important subalgebra chains are identified: spq(6,R)⊇suq(3)⊇soq(3) and spq(6,R) ⊇ spq2(2,R) ⊕ soq(3). The basis states of the q-deformed oscillator are classified according to these subalgebras. Finally, the Hamiltonian eigenvalues are discussed.
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