Convergent expansions for tunneling

Pierre VAN BAAL

Assa Auerbach, Steven Allan Kivelson

A. S. Bhullar, R. Blümel, Patrick M. Koch

Direct periodic-orbit expansions of individual spectral eigenvalues is a new direction in quantum mechanics. Using a unitary -matrix theory, we present exact, convergent, integral-free ghost orbit expansions of spectral eigenvalues for a step potential in the tunneling regime. We suggest an experiment to extract ghost orbit information from measured spectra in the tunneling regime (ghost orbit spectroscopy). We contrast our unitary, convergent theory with a recently published nonunitary, divergent theory [Yu. Dabaghian and R. Jensen, Eur. J. Phys. 26, 423 (2005)].

Francisco Marcelo Fernández

We calculate accurate tunnel resonances by means of standard Rayleigh–Schrödinger perturbation theory, exactly as if they were ordinary bound states. We choose one-dimensional barriers with a single maximum to test the convergence properties of the perturbation series. The method consists of an expansion of the potential-energy function about its maximum and a dilatation of the coordinate by means of a complex scaling parameter completely determined by the curvature of the barrier.

G. Nimtz, Astrid Haibel, A. A. Stahlhofen +1 more

Raphael David Levine