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

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

2005-01-12

arxiv.org/abs/quant-ph/0501054v1

Physics

Quantum Physics

54 pages, 3 figures given separately

Scientific paper

10.1007/s10955-005-5476-9

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.

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