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Elementare Quantenchemie by Hans Primas, Ulrich Müller-Herold

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By Hans Primas, Ulrich Müller-Herold

Das Buch gibt eine mathematisch elementare Einführung in die molekulare Quantenmechanik. Dabei stehen die chemisch wichtigen Aspekte im Vordergrund. Die relevanten Konzepte werden so weit als möglich intuitiv und ohne mathematische Pedanterie vermittelt, so daß ein erfolgreiches Studium des Buches mit Grundkenntnissen der research, der allgemeinen Physik und minimalen Fertigkeiten der Matrixrechnung möglich sein sollte. Obwohl keine höhere mathematischen Hilfsmittel verwendet werden, geht die Darstellung vor allem begrifflich weiter, als dies bei Einführungen in die Quantenchemie sonst üblich ist. Mehr als fünfzig, mit ausführlichen Lösungen versehene, Übungsaufgaben ergänzen den Haupttext und vermitteln anhand konkreter Beispiele Vertrautheit mit den neuen Begriffen.

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J 1,. " ,n 6 pik P, j f. für + P2+ ... +Pn k 1 einer erschöpfenden Klassifikation {P 1'" ,P n}legen die selbstadjungierten (nxn)Matrizen einer Matrixdarstellung nicht eindeutig fest. Unter den vielen Möglichkeiten ist am einfachsten eine Darstellung durch DiagonaZmatrizen. Eine Diagonalmatrix P kann die Relation p2=p nur erfüllen, wenn die Diagonalelemente der Gleichung P;a=P aa ' a=1, ... ,n, genügen, also wenn gilt P 00 = 0 oder P 00 = 1 Eine feinste Selektion resultiert, wenn genau ein Matrixelement Paa eins ist und alle andern verschwinden.

Und n=abzählbar unendlich). Eine andere in der Quantenmechanik wichtige Realisierung eines unendlichdimensionalen abstrakten Hilbertraumes ist diejenige durch komplexwertige quadratisch integrierbare Funktionen. )

Ii) und (iii) sind alte Bekannte für uns. • An eines selbstadjungierten Operators A mit nichtentarteten Eigenwerten definieren eine erschöpfende Klassifikation. • a nichtentartet. #a k für j#k. Die Voraussetzung n J der Nichtentartung ist notwendig. • an auseinanderzuhalten (anderenfalls resultiert eine nicht-erschöpfende Klassifikation). A A A Für eine erschöpfende Klassifikation müssen wir n paarweise orthogonale Projektoren angeben. Da diese aber auch durch einen selbstadjungierten Operator (mit nichtentartetem Spektrum) bestimmt sind.

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