Robert L. Intemann | Searcharxiv

arXiv2009

Comment on "Quantum mechanical versus semiclassical tunneling and decay times"

Shegelski, Kavka, and Hynbida have developed a method for calculating the lifetime of a particle initially localized in a potential well exactly quantum mechanically by employing a heuristic expression for the lifetime . Their method allows for the inclusion of a bound state, and their results for tunneling through a centrifugal barrier demonstrate the major role that bound states play in determining the lifetime. In this comment, I show that one can greatly simplify the analysis by calculating ^(1/2) instead. Results obtained are exact when no bound state is present. In the presence of a bound state the results are only approximate but still illustrate the influence that the presence of a bound state has on the lifetime.

quant-ph↗

arXiv2007

Comment on "On an identity for the volume integral of the square of a vector field"

Stewart has provided a position-space derivation of an identity for the volume integral of the square of a vector field that was quoted by Gubarev, Stodolsky and Zakharov. In this comment, I provide a momentum-space derivation of this result, generalized to the scalar product of two complex vector fields. This approach demonstrates the effective use of the Fourier transform technique in the context of vector analysis at a level suitable for undergraduate instruction.

physics.class-ph↗