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Open AccessArticle

A Full-Fledged Analytical Solution to the Quantum Harmonic Oscillator for Undergraduate Students of Science and Engineering

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Instituto de Física, Universidad Nacional Autónoma de México, Ciudad de México 04510, Mexico
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Facultad de Ingeniería, DCB, Universidad Nacional Autónoma de México, Ciudad de México 04510, Mexico
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Author to whom correspondence should be addressed.
Physics 2020, 2(4), 541-570; https://doi.org/10.3390/physics2040031
Received: 11 September 2020 / Revised: 2 October 2020 / Accepted: 2 October 2020 / Published: 17 October 2020
(This article belongs to the Section Physics Education)
The quantum harmonic oscillator is a fundamental piece of physics. In this paper, we present a self-contained full-fledged analytical solution to the quantum harmonic oscillator. To this end, we use an eight-step procedure that only uses standard mathematical tools available in natural science, technology, engineering and mathematics disciplines. This solution is accessible not only for physics students but also for undergraduate engineering and chemistry students. We provide interactive web-based graphs for the reader to observe the shape of the wave functions for an electron and a proton when both are subject to the same potential. Each of the eight steps in our solution procedure is treated as a separate problem in order to allow the reader to quickly consult any step without the need to review the entire article.
Keywords: quantum harmonic oscillator; full-fledged analytical solution; interactive wave functions quantum harmonic oscillator; full-fledged analytical solution; interactive wave functions
MDPI and ACS Style

Rodríguez-Gómez, A.; Pérez-Martínez, A.L. A Full-Fledged Analytical Solution to the Quantum Harmonic Oscillator for Undergraduate Students of Science and Engineering. Physics 2020, 2, 541-570.

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