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TMF, 2014, Volume 179, Number 1, Pages 36–77 (Mi tmf8618)  

Generalized oscillator representations for generalized Calogero Hamiltonians

B. L. Voronov, I. V. Tyutin

Lebedev Physical Institute, RAS, Moscow, Russia

Abstract: 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

DOI: https://doi.org/10.4213/tmf8618

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English version:
Theoretical and Mathematical Physics, 2014, 179:1, 416–451

Bibliographic databases:

Received: 24.11.2013

Citation: B. L. Voronov, I. V. Tyutin, “Generalized oscillator representations for generalized Calogero Hamiltonians”, TMF, 179:1 (2014), 36–77; Theoret. and Math. Phys., 179:1 (2014), 416–451

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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