Convergent Iterative Solutions for a Sombrero-Shaped Potential in Any Space Dimension and Arbitrary Angular Momentum

Abstract

We present an explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with an $N$-dimensional radial potential $V=\frac{g^2}{2}(r^2-1{)}^2$ and an angular momentum $l$. For $g$ large, the rate of convergence is similar to a power series in $g^{-1}$.

44 pages for text, 3 figures

References in corpus (4)

• Instanton -- Antiinstanton interaction and asymptotics of perturbation theory expansion in double well oscillator
• A Convergent Iterative Solution of the Quantum Double-well Potential
• New Ways to Solve the Schroedinger Equation
• A New Approach to Solve the Low-lying States of the Schroedinger Equation

Cited by in corpus (6)

• Convergent Iterative Solutions of Schroedinger Equation for a Generalized Double Well Potential
• Iterative Solutions for Low Lying Excited States of a Class of Schroedinger Equation
• General comparison theorems for the Klein-Gordon equation in d dimensions
• Sharp comparison theorems for the Klein--Gordon equation in $d$ dimensions
• Two Kinds of Iterative Solutions for Generalized Sombrero-shaped Potential in $N$-dimensional Space
• Groundstate with Zero Eigenvalue for Generalized Sombrero-shaped Potential in $N$-dimensional Space