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Absence of ground states for anions

Yukimi Goto

Abstract

We show that the $N$-electron Hamiltonian $H(N, Z)$ with the total nuclear charge $Z$ has no normalizable ground state if the ground state energy $E(N, Z)$ satisfies $E(N, Z)= E(N-1, Z)$ for $Z=N-1$. For anions $\mathrm{He}^-, \mathrm{Be}^-, \mathrm{N}^-, \mathrm{Ne}^-$, etc., many numerical results give strong evidence of the condition $E(N, Z)= E(N-1, Z)$.

Absence of ground states for anions

Abstract

We show that the -electron Hamiltonian with the total nuclear charge has no normalizable ground state if the ground state energy satisfies for . For anions , etc., many numerical results give strong evidence of the condition .
Paper Structure (2 sections, 3 theorems, 34 equations)

This paper contains 2 sections, 3 theorems, 34 equations.

Table of Contents

  1. Introduction
  2. Proof of the Main Theorem

Key Result

Theorem 1.1

Suppose $E(N, N-1) = E(N-1, N-1)$. Then $H(N, N-1)$ has no normalizable ground state in $L^2_a(\mathbb{R}^{3N})$.

Theorems & Definitions (4)

  • Theorem 1.1
  • Lemma 2.1
  • proof
  • Lemma 2.2: Kato Kato2