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Student Class

2027

Student Affiliation

WISP Intern

First Advisor

Rufus Boyack

First Advisor Department

Department of Physics and Astronomy

Description

This project aims to analyze the bound-state solutions of the one-dimensional pseudoharmonic oscillator potential. Past literature has suggested that bound-state solutions exist only when the coupling constant is greater than or equal to negative one quarter. However, previous research using matrix mechanics and a transcendental Kummer function has discovered bound-state solutions in the region less than negative one quarter. The wave functions of these solutions will be extensively studied by analyzing the limiting form of their probability distribution to understand the origins of these singular energies. Additionally, the expectation values of these wave functions will be analyzed, considering that the singular bound-state wave functions are not peaked at the origin. This analysis will also extend to a modified version of the hydrogen atom to investigate if it exhibits similar behavior. These analyses will offer insights into the essential mathematical properties of singular potentials in one dimension and explore the existence of a universal probability distribution for such states in singular one-dimensional potentials.

Publication Date

2024

Keywords

Harmonic Oscillator, Singular Potential

Disciplines

Quantum Physics

Singular bound states in the 1D pseudoharmonic oscillator

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