# Paul E. Shanley

**Associate Professor Emeritus
Theoretical Physics**

**B.S., Northeastern University, 1960
M.S., ibid., 1962
Ph.D., ibid., 1966**

E-mail: pshanley (at) nd (dot) edu

Address: Nieuwland Science Hall 402C

Phone: (574-63)1-6386

Fax: (574-63)1-5952

#### Research Interests

The properties of non-linear mechanical systems that exhibit chaotic behavior have been studied extensively in recent years. This has led to the question of whether such systems also exhibit chaos when governed by the laws of quantum mechanics. A particular feature seen in stationary quantum problems that are classically chaotic is an irregular spectrum of energy levels that is very sensitive to small changes in the potential. One area of interest by Prof. Shanley’s group is the study of the analytic properties of the quantum spectrum of such potentials to determine what singularities underlie the irregular spectrum.

#### Selected Publications

“Spectral Properties of the Scaled Quartic Anharmonic Oscillator,” Annals of Physics **186**, 292 (1988).

“Double Wells, Inverted Wells, and Level Crossing,” Phys. Lett. A **141**, 331 (1989).

“Diabolical Points and Their Relations to Level Crossing,” Phys. Lett. A **150**, 55 (1990).

Full Curriculum Vitae (pdf)