Geodesic
Discrete spectrum of Hamiltonians of some quantum system models
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 44-64 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the discrete spectrum of the Hamiltonian $H_0[Z_1]$ of relative motion of an $n$-particle quantum system $Z_1$ consisting of mutually identical particles of two types. The interaction of the first-type particles is described by a short-range potential $W_1$, the interaction of the second-type particles is described by a long-range potential $W_2$, and the interaction of particles of different types is described by a negative long-range potential $W_3$. Under some assumptions about the potentials $W_2$ and $W_3$, we demonstrate that the discrete spectrum of the operator $H_0[Z_1]$ is infinite both with and without taking the permutation symmetry into account.
Keywords: multiparticle Hamiltonian, discrete spectrum, permutation symmetry, mathematical quantum system model. 
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     author = {G. M. Zhislin},
     title = {Discrete spectrum of {Hamiltonians} of some quantum system models},
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     pages = {44--64},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a4/}
}
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G. M. Zhislin. Discrete spectrum of Hamiltonians of some quantum system models. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 44-64. http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a4/

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