Article Outline

Date: 2015-10-07; view: 645.

Abstract

R. Friedberg and T.D. Lee

^aDepartment of Physics, Columbia University, New York, NY 10027, USA
^bChina Center of Advanced Science and Technology (CCAST) (World Laboratory), P.O. Box 8730, Beijing 100080, People's Republic of China
^cRIKEN BNL Research Center (RBRC), Brookhaven National Laboratory, Upton, NY 11973, USA

Received 27 July 2004; accepted 5 August 2004. Available online 15 December 2004.

We discuss a new approach to solve the low lying states of the Schroedinger equation. For a fairly large class of problems, this new approach leads to convergent iterative solutions, in contrast to perturbative series expansions. These convergent solutions include the long standing difficult problem of a quartic potential with either symmetric or asymmetric minima.

1. Introduction

2. Construction of trial functions

2.1. A new formulation of perturbative expansion

2.2. Trial function for the quantum double-well potential

3. Hierarchy theorem and its generalization

4. Asymmetric quartic double-well problem

4.1. Construction of the first trial function

4.2. Construction of the second trial function

4.3. Symmetric vs asymmetric potential

5. The N-dimensional problem

Appendix A. A soluble example

A.1. A two-level model

A.2. Square-well example (Cont.)

A.3. The iterative sequence

References