Title: Convergence of the Quantum Mechanical Perturbation Series<br>

Abstract: The general theme of the talk will be the convergence properties of
series arising from perturbative calculation in nonrelativistic quantum
mechanics and relativistic quantum field theory. The main example will
be the series for the ground state energy of the quantized simple
harmonic oscillator with a small fourth degree anharmonicity. I will
give a heuristic proof of the divergence of the perturbation series in
this case and will proceed to discuss the asymptotic nature of the series
in a simplified example. Finally, I will introduce the method of Borel
summation, which provides a natural way to resum certain asymptotic
series to obtain a convergent result.