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Lehrbuch der Mathematischen Physik

Lehrbuch der Mathematischen Physik

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Springer Nature
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9783211825358
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In der Quantentheorie werden Observable durch Operatoren im Hilbert-Raum dargestellt. Der dafr geeignete mathematische Rahmen sind die Cx - Algebren, welche Matrizen und komplexe Funktionen verallgemeinern. Allerdings bentigt man in der Physik auch unbeschrnkte Operatoren, deren Problematik eigens untersucht werden mu. Dementsprechend werden zunchst mathematische Fragen studiert und dann die Methoden auf atomare Systeme angewandt. Obgleich man auer dem Wasserstoffatom kaum explizit lsbare Probleme findet, lassen sich nicht nur allgemeine qualitative Fragen, etwa bezglich des Energiespektrums und Streuverhaltens, beantworten, sondern auch quantitativ kann man auch fr kompliziertere Systeme fr mebare Gren Schranken teils befriedigender Genauigkeit finden. Inhaltsverzeichnis: Einleitung: Die Struktur der Quantentheorie; Grenordnungen atomarer Systeme.- Die mathematische Formulierung der Quantenmechanik: Lineare Rume; Algebren; Darstellungen im Hilbertraum; Einparametrige Gruppen; Unbeschrnkte Operatoren und quadratische Formen.- Quantendynamik: Das Weyl-System; Der Drehimpuls; Die Zeitentwicklung; Der Limes t ; Strungstheorie; Stationre Streutheorie.- Atomare Systeme: Das Wasserstoffatom; Das H-Atom in ueren Feldern; Heliumartige Atome; Streuung am einfachen Atom; Komplexe Atome; Kernbewegung und einfache Molekle.

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