Explicit Green operators for quantum mechanical Hamiltonians.~II.~ Edge\n type singularities of the helium atom

2018/01/23 by Heinz‐Juergen Flad, Flad, Heinz-Juergen, Gohar Flad‐Harutyunyan +3
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Advanced Chemical Physics Studies #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.1801.07552

Abstract

We extend our approach of asymptotic parametrix construction for Hamiltonian\noperators from conical to edge-type singularities which is applicable to\ncoalescence points of two particles of the helium atom and related two electron\nsystems including the hydrogen molecule. Up to second order we have calculated\nthe symbols of an asymptotic parametrix of the nonrelativisic Hamiltonian of\nthe helium atom within the Born-Oppenheimer approximation and provide explicit\nformulas for the corresponding Green operators which encode the asymptotic\nbehaviour of the eigenfunctons near an edge.\n

Related

• Ellipticity of quantum mechanical Hamiltonians in the edge algebra
• Explicit Green operators for quantum mechanical Hamiltonians. I. The\n hydrogen atom
• Harmonic oscillator model for the helium atom
• Asymptotic Parametrices of Elliptic Edge Operators
• Analytical solution of the Schrodinger equation for the neutral helium atom in the ground state considering the uncertainty principle, vibrational modes and quantum-electrodynamical effects