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Electron wavefunctions and densities for atoms. (English) Zbl 0985.81133
Summary: With a special ‘Ansatz’ we analyze the regularity properties of atomic electron wavefunctions and electron densities. In particular, we prove an a priori estimate, $\sup_{y\in B(x,R)}|\nabla\psi(y)|\leq C(R)\sup_{y\in B(x,2R)}|\psi(y)|$ and obtain for the spherically averaged electron density, $$\widetilde\rho(r)$$, that $$\widetilde\rho''(0)$$ exists and is nonnegative.

##### MSC:
 81V45 Atomic physics 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 35B45 A priori estimates in context of PDEs 35Q40 PDEs in connection with quantum mechanics
##### Keywords:
a priori estimate
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