BOUND STATE ENERGY OF DELTA-FUNCTION POTENTIAL: A NEW REGULARIZATION SCHEME (RESEARCH NOTE)

Siti Rohayati, Iwan Setiawan, Eko Risdianto

Sami M. Al-Jaber

R. Jackiw

Horacio E. Camblong, CARLOS R. ORDÓÑEZ

A path-integral approach for \ensuremath{\delta}-function potentials is presented. Particular attention is paid to the two-dimensional case, which illustrates the realization of a quantum anomaly for a scale-invariant problem in quantum mechanics. Our treatment is based on an infinite summation of perturbation theory that captures the nonperturbative nature of the \ensuremath{\delta}-function bound state. The well-known singular character of the two-dimensional \ensuremath{\delta}-function potential is dealt with by considering the renormalized path integral resulting from a variety of schemes: dimensional, momentum-cutoff, and real-space regularization. Moreover, compatibility of the bound-state and scattering sectors is shown.

Nikolay N. Bogolubov, Alexey N. Kireev

A general variational method is proposed for investigating the surface polaron ground state valid for any coupling strength of an electron-surface-optical-phonon interaction and for any height of a barrier potential at the crystal boundary. The ground states of the surface polaron at the infinitely high barrier potential and of the surface polaron without the barrier potential are considered. The properties of the surface polarons are discussed in comparison with the bulk polaron theory.

A. Ronveaux