It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one
that has a positive-definite spectrum and obeys the requirement of unitarity) must be …

We present an abstract perturbation theory for operators of the form H 0+ V obeying four
properties:(1) H 0 is a positive self-adjoint operator on L 2 (M, μ) with μ a probability …

We present a method in which the Padé approximant is used to calculate the asymptotic
behavior of a function from the first few terms of its power series. We illustrate this method by …

This book explains the fundamental concepts and theoretical techniques used to understand
the properties of quantum systems having large numbers of degrees of freedom. A number …

These notes are based on the course of lectures I gave at Harvard in the fall of 1964. They
constitute a self-contained account of vector bundles and K-theory assuming only the …

This paper is concerned with the nature of perturbation theory in very high order.
Specifically, we study the Rayleigh-Schrödinger expansion of the energy eigenvalues of the …

This is a comprehensive exposition of the classical moment problem using methods from the
theory of finite difference operators. Among the advantages of this approach is that the …

We study the analytic properties of the singular perturbation theory for p 2+ x 2+ βx 4. We
prove rigorously several of the properties of the energy levels, previously found by C …

We examine the large-order behavior of perturbation theory for the anharmonic oscillator, a
simple quantum-field-theory model. New analytical techniques are exhibited and used to …

We study the perturbation theory for H= p 2+ x 2+ β x 2 n+ 1, n= 1, 2,.... It is proved that when
Imβ≠ 0, H has discrete spectrum. Any eigenvalue is uniquely determined by the (divergent) …