Paolo Moretti

Propagator for finite range potentials

The Schrodinger equation in integral form is applied to the one-dimensional scattering problem in the case of a general finite range, nonsingular potential. A simple expression for the Laplace transform of the transmission propagator is obtained in terms of the associated Fredholm determinant, by means of matrix methods; the particular form of the kernel and the peculiar aspects of the transmission problem play an important role. The application to an array of delta potentials is shown.

Inversion time of large spins

In order to find an accurate expression for the inversion probability of a large spin, an asymptotic expansion in series of Bessel functions is found, and a formula for the inversion time is obtained.

Quantum dynamics of a particle interacting with a double barrier

Following a previously developed method, the problem of a particle scattered by a double barrier is studied. Instead of the simple transmission or reflection, the more difficult case of the arrival in the region between the barriers is considered and solved explicitly by using matrix methods.

On a class of integral equations having application in quantum dynamics

A class of Fredholm integral equations of the second kind is studied, with kernel separable outside the basic interval (a, b). Using theorems of matrix algebra, the solution for x outside (a, b) is found in terms of the Fredholm determinants in a simple and compact form. As a particular case, the quantum propagator for one-dimensional problems is obtained.

Propagator for finite range potentials : The case of reflection

Following a previous study on the transmission propagator for a finite range potential, the problem of reflection is considered. It is found that the Laplace transform of the reflection propagator can be expressed in terms of the usual Fredholm determinant Δ and of a new similar determinant Γ, containing the peculiar characteristics of reflection. As an example, an array of delta potentials is considered. Moreover, a possible application to the calculation of quantum traversal time is shown.

The asymptotic calculation of Wiener integrals occurring in quantum and statistical physics: A divergency problem

The asymptotic expression of a Wiener functional integral using the eigenvalues of the associated Sturm–Liouville equation is obtained, correcting previous formulas giving a divergent result.