A New Approach to Solve the Low-lying States of the Schroedinger Equation

Abstract

We review a new iterative procedure to solve the low-lying states of the Schroedinger equation, done in collaboration with Richard Friedberg. For the groundstate energy, the $n^{th}$ order iterative energy is bounded by a finite limit, independent of $n$; thereby it avoids some of the inherent difficulties faced by the usual perturbative series expansions. For a fairly large class of problems, this new procedure can be proved to give convergent iterative solutions. These convergent solutions include the long standing difficult problem of a quartic potential with either symmetric or asymmetric minima.

54 pages, 3 figures given separately

References in corpus (2)

• A Convergent Iterative Solution of the Quantum Double-well Potential
• New Ways to Solve the Schroedinger Equation

Cited by in corpus (2)

• Convergent Iterative Solutions for a Sombrero-Shaped Potential in Any Space Dimension and Arbitrary Angular Momentum
• Iterative Solutions for Low Lying Excited States of a Class of Schroedinger Equation