Geodesic
Spectral Properties of Hamiltonians of Charged Systems in a Homogeneous Magnetic Field: I. General Characteristic of the Spectrum
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 1, pp. 87-102 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the spectrum of Hamiltonians of charged multiparticle systems in a homogeneous magnetic field with a fixed sum $P_{\Sigma }$ of the pseudomomentum components and without it. We prove that if $P_{\Sigma }$ is fixed, then the spectrum of Hamiltonians is independent of the value of $P_{\Sigma }$, while the spectrum without fixation of $P_{\Sigma }$ coincides with the spectrum with fixation and differs from the latter only by some additional infinite degeneration (this is a principal difference between problems with a homogeneous magnetic field and problems without any field in which the absence of any fixation of the total angular momentum results in “covering” the spectrum of the relative motion by a continuous spectrum). We find the continuous spectrum of the Hamiltonians and characterize the spectrum of Hamiltonians of two-cluster mutually noninteracting systems obtained by decomposing the original system in the state with a fixed value of $P_{\Sigma }$. The last result is necessary for the study of the purely point spectrum.
Keywords: Hamiltonian, homogeneous magnetic field, spectral properties, relative motion, pseudomomentum. 
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     author = {G. M. Zhislin},
     title = {Spectral {Properties} of {Hamiltonians} of {Charged} {Systems} in {a~Homogeneous} {Magnetic} {Field:} {I.~General} {Characteristic} of the {Spectrum}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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G. M. Zhislin. Spectral Properties of Hamiltonians of Charged Systems in a Homogeneous Magnetic Field: I. General Characteristic of the Spectrum. Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 1, pp. 87-102. http://geodesic.mathdoc.fr/item/TMF_2002_133_1_a5/

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