John Ray Martinez

John is an AWS Certified Machine Learning Specialist with experience in recommendation systems, NLP, and time series. He is a recipient of Outstanding Graduate Student Award, College of Computing & Informatics Drexel University in 2021. He is a Data Professional with more than a decade of software engineering experience and a teaching background in Physics.

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John Ray Martinez and Ermys Bornilla
Samahang Pisika ng Visayas at Mindanao (SPVM) (2008): 99-102.

Wigner distribution for n=6 energy eigestate in the Csc<sup>2</sup>(x).

Abstract. The Wigner distribution of a particle subject to the cosecant squared potential, V(x) = Csc2(x), is calculated. Cosecant squared potential is among the non-trivial potential that cannot be solved exactly. However, this potential is known to be the supersymmetric (SUSY) partner potential of the infinite square well. Thus, the position and momentum wavefunctions of Cosecant squared potential for some values of n are evaluated with the use of Mathematica 5.2. With these, the Wigner distribution can be determined. In this work, this distribution is plotted in phase-space wherein negative probabilities are observed. It is shown that several properties of Wigner function are observed to be similar to probability density; i.e. it is called Wigner Quasi-probability distribution.

The full paper can be downloaded here.

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