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Ground State of the Polaron Hydrogenic Atom in a Strong Magnetic Field

Rohan Ghanta

Abstract

The ground-state electron density of a polaron bound to a Coulomb potential in a homogeneous magnetic field--the transverse coordinates integrated out--converges pointwise and weakly in the strong magnetic field limit to the square of a hyperbolic secant function.

Ground State of the Polaron Hydrogenic Atom in a Strong Magnetic Field

Abstract

The ground-state electron density of a polaron bound to a Coulomb potential in a homogeneous magnetic field--the transverse coordinates integrated out--converges pointwise and weakly in the strong magnetic field limit to the square of a hyperbolic secant function.

Paper Structure

This paper contains 14 sections, 26 theorems, 131 equations.

Table of Contents

  1. Introduction
  2. Model and Main Result
  3. Differentiating the One-Dimensional Energy
  4. Upper Bound to the Ground-State Energy
  5. Lower Bound to the Ground-State Energy
  6. Delta-function potential
  7. Concentration in the Lowest Landau Level
  8. Proof of Proposition \ref{['prop: ending proposition']}.
  9. Reduction to one dimension
  10. Localization and decomposition.
  11. Error estimates
  12. Proof of Theorem \ref{['thm:Wavefunction']}
  13. Compactness of Minimizing Sequences
  14. Bound on the Effective Coulomb Potential

Key Result

Theorem 2.1

Let $E_{0}(B)$ be as defined in (eq:2-1) above. Then

Theorems & Definitions (49)

  • Theorem 2.1
  • Theorem 2.2
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Theorem 3.3
  • proof
  • Theorem 4.1
  • Lemma 4.2
  • ...and 39 more