Generalized oscillator representations for generalized Calogero Hamiltonians
| Autor: | Tyutin, I. V., Voronov, B. L. |
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| Rok vydání: | 2013 |
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| Druh dokumentu: | Working Paper |
| Popis: | This paper is a natural continuation of the previous paper \cite{TyuVo13} where generalized oscillator representations for Calogero Hamiltonians with potential $V(x)=\alpha/x^2$, $\alpha\geq-1/4$, were constructed. In this paper, we present generalized oscillator representations for all generalized Calogero Hamiltonians with potential $V(x)=g_{1}/x^2+g_{2}x^2$, $g_{1}\geq-1/4$, $g_{2}>0$. These representations are generally highly nonunique, but there exists an optimum representation for each Hamiltonian, representation that explicitly determines the ground state and the ground-state energy. For generalized Calogero Hamiltonians with coupling constants $g_1<-1/4$ or $g_2<0$, generalized oscillator representations do not exist in agreement with the fact that the respective Hamiltonians are not bounded from below. Comment: 39 pages, LaTeX-2e. arXiv admin note: substantial text overlap with arXiv:1211.6331 |
| Databáze: | arXiv |
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