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Lehrbuch Der Mathematischen Physik: v. 4: Quantenmechanik Grosser Systeme

Lehrbuch Der Mathematischen Physik: v. 4: Quantenmechanik Grosser Systeme (Paperback)

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Synopsis

In der Quantentheorie werden Observable durch Operatoren im Hilbert-Raum dargestellt. Der dafA1/4r geeignete mathematische Rahmen sind die Cx - Algebren, welche Matrizen und komplexe Funktionen verallgemeinern. Allerdings benAtigt man in der Physik auch unbeschrAnkte Operatoren, deren Problematik eigens untersucht werden muA. Dementsprechend werden zunAchst mathematische Fragen studiert und dann die Methoden auf atomare Systeme angewandt. Obgleich man auAer dem Wasserstoffatom kaum explizit lAsbare Probleme findet, lassen sich nicht nur allgemeine qualitative Fragen, etwa bezA1/4glich des Energiespektrums und Streuverhaltens, beantworten, sondern auch quantitativ kann man auch fA1/4r kompliziertere Systeme fA1/4r meAbare GrAAen Schranken teils befriedigender Genauigkeit finden. Inhaltsverzeichnis: Einleitung: Die Struktur der Quantentheorie; GrAAenordnungen atomarer Systeme.- Die mathematische Formulierung der Quantenmechanik: Lineare RAume; Algebren; Darstellungen im Hilbertraum; Einparametrige Gruppen; UnbeschrAnkte Operatoren und quadratische Formen.- Quantendynamik: Das Weyl-System; Der Drehimpuls; Die Zeitentwicklung; Der Limes t; StArungstheorie; StationAre Streutheorie.- Atomare Systeme: Das Wasserstoffatom; Das H-Atom in AuAeren Feldern; Heliumartige Atome; Streuung am einfachen Atom; Komplexe Atome; Kernbewegung und einfache MolekA1/4le.

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