Spectral problem for the mean field Hamiltonian
Articles
Arvydas Astrauskas
Institute of Mathematics and Informatics
Published 2021-06-15
https://doi.org/10.15388/LMR.2007.24252
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Keywords

mean field difference operator
eigenvalue problem
characteristic equation for eigenvalues
linear differential equations
spectral representation of solutions

How to Cite

Astrauskas, A. (2021) “Spectral problem for the mean field Hamiltonian”, Lietuvos matematikos rinkinys, 47(spec.), pp. 503–507. doi:10.15388/LMR.2007.24252.
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Vol. 47 (2007)

Spectral problem for the mean field Hamiltonian

Abstract

We consider the mean field Hamiltonian HV = κ ΔV + ξ(·) in l2(V ), where V = {x} is a finite set. Characteristic equations for eigenvalues and expressions for eigenfunctions of HV are obtained. Using this result, the spectral representation of the solution of the corresponding ("head transition'') differential equation is derived.

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