The regularity of electronic wave functions in Barron spaces

Key Points

• To investigate the regularity of electronic wave functions within Barron spaces for negative eigenvalues beneath the essential spectrum.
• Analyzed solutions of the electronic Schrödinger equation.
• Explored properties of wave functions in the context of Coulomb interactions.
• Assessed examples, including the hydrogen ground state, to illustrate findings.
• Demonstrated that solutions for negative eigenvalues exist in spectral Barron spaces $B^s$ for $s<1$.
• Showed that the result is optimal, as exemplified by the hydrogen ground state.