相关论文: Stark Effect in Lax-Phillips Theory

The main mathematical manifestation of the Stark effect in quantum mechanics is the shift and the formation of clusters of eigenvalues when a spherical Hamiltonian is perturbed by lower order terms. Understanding this mechanism turned out…

In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star-product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical…

In this paper we prove the existence of the Stark-Wannier quantum resonances for one-dimensional Schrodinger operators with smooth periodic potential and small external homogeneous electric field. Such a result extends the existence result…

A partial-wave method is developed to deal with small molecules dominated by a central atom as an extension of earlier single-center methods. In particular, a model potential for the water molecule is expanded over a basis of spherical…

In this third of a series of four articles, we continue the study of the representations of the hamiltonian dynamical transformations of systems of correlated quantized oscillators. By our use of generalized wave function solutions to…

Due to spectral obstructions, a scattering theory in the Lax-Phillips sense for the wave equation for differential p-forms on H^{n+1} cannot be developed. As a consequence, Huygens' principle for the wave equation in this context does not…

Infinitely rising one-dimensional potentials constitute impenetrable barriers which reflect totally any incident wave. However, the scattering by such kind of potentials is not structureless: resonances may occur for certain values of the…

The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…

Approximate scattering and bound state solutions of the one-dimensional effective-mass Dirac equation with the Woods-Saxon potential are obtained in terms of the hypergeometric-type functions. Transmission and reflection coefficients are…

In quantum physics, disturbance due to a measurement is not negligible. This requires the time parameter $t$ in the Schr\"odinger or Heisenberg equation to be considered differently from a time continuum of experimenter's clock $T$ on which…

In non-relativistic quantum mechanics, singular potentials in problems with spherical symmetry lead to a Schrodinger equation for stationary states with non-Fuchsian singularities both as r tends to zero and as r tends to infinity. In the…

The Helmholtz equation in one dimension, which describes the propagation of electromagnetic waves in effectively one-dimensional systems, is equivalent to the time-independent Schr\"odinger equation. The fact that the potential term…

The Schrodinger equation for stationary states in a central potential is studied in an arbitrary number of spatial dimensions, say q. After transformation into an equivalent equation, where the coefficient of the first derivative vanishes,…

The quantum resonances occurring with delta-kicked particles are studied with the help of a fictitious classical limit, establishing a direct correspondence between the nearly resonant quantum motion and the classical resonances of a…

Resonances, or scattering poles, are complex numbers which mathematically describe meta-stable states: the real part of a resonance gives the rest energy, and its imaginary part, the rate of decay of a meta-stable state. This description…

The explanation of the first-order Stark effect in hydrogen by Epstein and Schwarzschild in 1916 was seen as a great success for the old quantum theory. Yet, it also revealed some serious limitations of the theory. To recover the…

In this paper we present the connection between scattering amplitudes in momentum space and wave functions in coordinate space, generalizing previous work done for s-waves to any partial wave. The relationship to the wave function of the…

It has been shown that quantum paradoxes have followed from one special assumption, i.e., from attributing basic physical meaning to Hamiltonian eigenfunctions and representing all physical states by vectors of the Hilbert space spanned on…

A scattering mechanism stemming from the Stark-shift of energy levels by electric fields in semiconductor quantum wells is identified. This scattering mechanism feeds off interface roughness and electric fields, and modifies the well known…

We show that the normalization integral for the Schr\"odinger and Dirac scattering wave functions contains, besides the usual delta-function, a term proportional to the derivative of the phase shift. This term is of zero measure with…