Geodesic
Generalized oscillator representations for generalized Calogero Hamiltonians
Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 1, pp. 36-77 Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct generalized oscillator representations for all generalized Calogero Hamiltonians with the potential $V(x)=g_1/x^2+g_2x^2$, $g_1\ge-1/4$, $g_2>0$. These representations are generically nonunique, but for each Hamiltonian, there exists an optimum representation explicitly determining the ground state and its energy. For generalized Calogero Hamiltonians with coupling constants $g_1<-1/4$ or $g_2<0$, generalized oscillator representations do not exist, which agrees with the fact that the corresponding Hamiltonians are not bounded from below.
Keywords: quantum mechanics, oscillator representation, self-adjoint Hamiltonian. 
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B. L. Voronov; I. V. Tyutin. Generalized oscillator representations for generalized Calogero Hamiltonians. Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 1, pp. 36-77. http://geodesic.mathdoc.fr/item/TMF_2014_179_1_a3/

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