Chirp-wave Expansion of the Electron Wavefunctions in Atoms

The description of the electron wavefunctions in atoms is generalized to the fractional Fourier series. This method introduces a continuous and infinite number of chirp basis sets with linear variation of the frequency to expand the wavefunctions, in which plane-waves are a special case. The chirp characteristics of each basis set can be adjusted through a single parameter. Thus, the basis set cutoff can be optimized variationally. The approach is tested with the expansion of the electron wavefunctions in atoms, and it is shown that chirp basis sets substantially improve the convergence in the description of the electron density. We have found that the natural oscillations of the electron core states are efficiently described in chirp-waves

Rafael Torres, Jr. - Does the United States Supreme Court decision in the \u3cem\u3eCitizens United v. the Federal Election Commission\u3c/em\u3e case affect the voluntary departure of United States Senators

The United States Supreme Court decision in the case of Citizens United v. the Federal Election Commission raised concerns about how unlimited independent expenditures by organizations would influence campaigns and elections. This concern has been expressed through media and politicians, but research on the subject is conflicting. One argument is that protecting unlimited contributions as free speech gives a disproportionate amount of speech to non-voting entities. The other argument is that speech does not directly influence elections and it is ultimately the voter\u27s decision on which candidate to choose. Laws that affect elections also affect departures. The connection between campaign finance and Senate departures is that a change in the law will affect election outcomes causing more Senators to voluntarily depart from Congress in anticipation of a contentious election. I am studying the 108-113th Congresses to determine if there is a difference in Senate departures before and after the decision. Voluntary departure includes retirement, resignation, and moving to another public office. The differences in departure will be determined by changes in the rate of departure and the profiles of voluntarily departing Senators. If the court\u27s decision has made elections more competitive then there should be an increase in Senate departures. The study examines the differences before and after the Citizens United ruling based on age, the number of years of service in the Senate, and the last election win margin. I will lastly discuss possible future empirical research on Congressional retirements as well as post-Senate career profiles.https://epublications.marquette.edu/mcnair_2013/1003/thumbnail.jp