Harnessing the Matrix Method with SMath to Explore the Finite Square Well Potential

Chittaranjan Ghosh; Koustav Dey

doi:10.59573/emsj.8(2).2024.20

Authors

Chittaranjan Ghosh
Koustav Dey

DOI:

https://doi.org/10.59573/emsj.8(2).2024.20

Keywords:

SMath Studio, finite square well potential, infinite square well potential, matrix method

Abstract

This innovative research makes use of a matrix-method driven numerical voyage into the foundation of the time-independent Schr?dinger equation for a one-dimensional finite square well potential to unlock the secrets of the quantum realm. This is made possible by the unmatched power of the open-source computational juggernaut, SMath Studio. The work unfolds the quantum tapestry by cleverly placing the finite square well inside the infinitely large potential of an infinite square well, using an infinite number of basis vectors to invoke wavefunctions from the very fabric of the universe. This scholarly masterwork not only clarifies the elusive low-lying bound states of the finite square well potential but also acts as a quantum lighthouse, illuminating the complex quantum landscape for undergraduate students with unmatched clarity and understanding.

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