arXiv subjects

Robert Grummt

Publications and source records attributed to Robert Grummt.

3 recordsLinked to original sources

arXiv2017

On the Dipole Approximation with Error Estimates

The dipole approximation is employed to describe interactions between atoms and radiation. It essentially consists of neglecting the spatial variation of the external field over the atom. Heuristically, this is justified by arguing that the wavelength is considerably larger than the atomic length scale, which holds under usual experimental conditions. We prove the dipole approximation in the limit of infinite wavelengths compared to the atomic length scale and estimate the rate of convergence. Our results include N-body Coulomb potentials and experimentally relevant electromagnetic fields such as plane waves and laser pulses.

math-ph↗

arXiv2011

On the Time-Dependent Analysis of Gamow Decay

Gamow's explanation of the exponential decay law uses complex "eigenvalues" and exponentially growing "eigenfunctions". This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wave functions. Observing that the time evolution of any wave function is given by its expansion in generalized eigenfunctions, we shall answer this question in the most straightforward manner, which at the same time is accessible to graduate students and specialists. Moreover the presentation can well be used in physics lectures to students.

quant-ph↗

arXiv2009

On the Time-Dependent Analysis of Gamow Decay

Gamow's approach to exponential decay of meta-stable particles via complex 'eigenvalues' (resonances) of a Hamiltonian is scrutinized. We explain the sense in which the non-square-integrable 'eigenfunctions' that belong to these resonances (Gamow functions) are relevant for the time-evolution of square-integrable wave functions. For concreteness we study a one dimensional square-well potential with a trapping region K and the evolution of wave functions, whose support is initially inside of K. It is shown that the sum over the first few time-evolved Gamow functions restricted to K yields an approximation for the evolution of these initial wave functions within the trapping region. The approximation is good for all times for which exponential decay prevails.

math-ph↗