Analyticity of the density of electronic wavefunctions
英文摘要:
We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in ${\mathbb R}^3$ away from the nuclei.
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S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, T. Østergaard Sørensen
We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in ${\mathbb R}^3$ away from the nuclei.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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Expressing the Schroedinger Lagrangian ${\cal L}$ in terms of the quantum wavefunction $ψ=\exp(S+{\rm i}I)$ yields the conserved Noether current ${\bf J}=\exp(2S)\nabla I$. When $ψ$ is a stationary state, the divergence of ${\bf J}$ vanishes. One can exchange $S$ with $I$ to obtain a new Lagrangian $\tilde{\cal L}$ and a new Noether current $\tilde{\bf J}=\exp(2I)\nabla S$, conserved under the equations of motion of $\tilde{\cal L}$. However this new current $\tilde{\bf J}$ is generally not conserved under the equations of motion of the original Lagrangian ${\cal L}$. We analyse the role playe…
We prove analytic-type estimates in weighted Sobolev spaces on the eigenfunctions of a class of elliptic and nonlinear eigenvalue problems with singular potentials, which includes the Hartree-Fock equations. Going beyond classical results on the analyticity of the wavefunctions away from the nuclei, we prove weighted estimates locally at each singular point, with precise control of the derivatives of all orders. Our estimates have far-reaching consequences for the approximation of the eigenfunctions of the problems considered, and they can be used to prove a priori estimates on the numerical s…
We consider an electronic bound state of the usual, non-relativistic, molecular Hamiltonian with Coulomb interactions and fixed nuclei. Away from appropriate collisions, we prove the real analyticity of all the reduced densities and density matrices, that are associated to this bound state. We provide a similar result for the associated reduced current density.Published: J. Math. Phys. 63, 013509 (2022); https://doi.org/10.1063/5.0056488
We give a new, short proof of the regularity away from the nuclei of the electronic density of a molecule obtained in [1,2]. The new argument is based on the regularity properties of the Coulomb interactions underlined in [3,4] and on well-known elliptic technics. [1] S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, T. Oe stergaard Soerensen: The electron density is smooth away from the nuclei. Comm. Math. Phys. 228, no. 3 (2002), 401-415. [2] S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, T. Oestergaard Soerensen: Analyticity of the density of electronic wave functions. Ark.…
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We prove that the electronic density of atomic and molecular eigenfunctions is smooth away from the nuclei. The result is proved without decay assumptions on the eigenfunctions.
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