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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
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