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Spectrum of the relative motion of many-particle systems in a homogeneous magnetic field: What do we know about it? (English) Zbl 0922.35103

Buslaev, V. (ed.) et al., Differential operators and spectral theory. M. Sh. Birman’s 70th anniversary collection. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 189(41), 275-285 (1999).
Summary: The relative motion of many-particle quantum systems in a homogeneous magnetic field is studied. We formulate new results on the behavior of discrete spectrum, obtained by the method of fixation of pseudomomentum. In particular, these results can be applied to the helium atom.
For the entire collection see [Zbl 0911.00011].

MSC:

35P05 General topics in linear spectral theory for PDEs
81V70 Many-body theory; quantum Hall effect
35J10 Schrödinger operator, Schrödinger equation
35Q40 PDEs in connection with quantum mechanics
81Q15 Perturbation theories for operators and differential equations in quantum theory
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