Markowich, Peter A. Boltzmann distributed quantum steady states and their classical limit. (English) Zbl 0788.35110 Forum Math. 6, No. 1, 1-33 (1994). Author’s summary: “We prove the existence and uniqueness of Boltzmann distributed quantum steady states of an electron ensemble which moves under the actions of the self consistent Coulomb potential and of an external potential. The case of the particles confined to a three- dimensional bounded domain and the whole space case in \(\mathbb{R}^ 3\) is analyzed. Also we prove the existence of the classical limit. As the Planck constant tends to zero we obtain a Maxwellian equilibrium solution of the Vlasov-Poisson problem”. Reviewer: P.Hillion (Le Vesinet) Cited in 5 Documents MSC: 35Q40 PDEs in connection with quantum mechanics 35P20 Asymptotic distributions of eigenvalues in context of PDEs 35Q60 PDEs in connection with optics and electromagnetic theory Keywords:Boltzmann distribution; quantum states; Coulomb potential; existence; uniqueness; Maxwellian equilibrium solution of the Vlasov-Poisson problem PDFBibTeX XMLCite \textit{P. A. Markowich}, Forum Math. 6, No. 1, 1--33 (1994; Zbl 0788.35110) Full Text: DOI EuDML