Das Weyl-Stonesche Eigenwertproblem

Günter Hellwig
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Günter Hellwig: Technischen Universität Berlin

Chapter V in Differentialoperatoren der mathematischen Physik, 1964, pp 191-239 from Springer

Abstract: Zusammenfassung Besteht unser quantenmechanisches System aus einem Atomkern und einem Elektron, so kommen wir in den Bezeichnungen aus IV.4.5 zu dem (Wasserstoff-) Operator (1) $$Au = - {\Delta _3}u - \frac{\delta }{{\left| x \right|}}u,{\text{ }}\delta = \frac{{8{\pi ^2}m{e^2}}}{{{h^2}}},$$ der in den Teilräumen (2) $$\mathop \mathfrak{A}\limits^ \circ = \{ u(x)\} |u \in C^2 (\Re _3 ),u \equiv 0{\text{f}}{\text{r }}|x| \geqslant R mit R = R(u)\}$$ (1) $$\mathfrak{A}_1 = \left\{ {u(x)|1.u \in C^0 (\Re _3 ) \cap C^2 \left( {\left| x \right| > 0} \right) \cap ,Au \in ;2.\left| u \right| \leqslant e^{ - \gamma r} ,\left| {u_{x_1 } } \right| \leqslant e^{ - \gamma r} , \ldots ,\left| {u_{x_s } } \right| \leqslant e^{ - \gamma r} furaller = \left| x \right| \leqslant r_0 mit\gamma = \gamma (u) > 0,r_0 = r_0 (u) > 0} \right\}$$ wesentlich selbstadjungiert ist.

Date: 1964
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DOI: 10.1007/978-3-642-92884-0_5

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