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Computational Physics (Part I) coursework: Computational Approach to Modelling the Schrödinger Equation in the Pöschl-Teller Potential Well.

Elsie Sheldrake

Published Jan 1, 2026• 0 citations
Publisher

Abstract

This work is from a coursework for Part I of my 10 credit Computational Physics module. This is not in a typical report style, instead being tailored to a set of four tasks approached with the various methods explored in this part of the course. The report serves to store an online portfolio of my work so far.The specific tasks addressed in this work were:Illustrating de-dimensionalisation of the one-dimensional Schrödinger equation subject to a Pöschl-Teller potential well.Finding numerically all localised eigenstates of this system.Implementation of a numerical method to simulate the dynamics of the given system, subject to specified initial conditions.Modifying the code from 3. to simulate a similar system, in which the potential has a small time-dependence.I was happy to achieve a mark of 100% for this report and its accompanying code, which can be found on my GitHub.

DOI
10.6084/m9.figshare.31742881

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This work is from a coursework for Part I of my 10 credit Computational Physics module. This is not in a typical report style, instead being tailored to a set of four tasks approached with the various methods explored in this part of the course. The report serves to store an online portfolio of my work so far.The specific tasks addressed in this work were:Illustrating de-dimensionalisation of the one-dimensional Schrödinger equation subject to a Pöschl-Teller potential well.Finding numerically all localised eigenstates of this system.Implementation of a numerical method to simulate the dynamics of the given system, subject to specified initial conditions.Modifying the code from 3. to simulate a similar system, in which the potential has a small time-dependence.I was happy to achieve a mark of 100% for this report and its accompanying code, which can be found on my GitHub.
This concise textbook introduces an innovative computational approach to quantum mechanics. Over the course of this engaging and informal book, students are encouraged to take an active role in learning key concepts by working through practical exercises. The book equips readers with some basic methodology and a toolbox of scientific computing methods, so they can use code to simulate and directly visualize how quantum particles behave. The important foundational elements of the wave function and the Schrödinger equation are first introduced, then the text gradually builds up to advanced topics including relativistic, open, and non-Hermitian quantum physics. This book assumes familiarity with basic mathematics and numerical methods, and can be used to support a two-semester advanced undergraduate course. Source code and solutions for every book exercise involving numerical implementation are provided in Python and MATLAB®, along with supplementary data. Additional problems are provided online for instructor use with locked solutions.
This concise textbook introduces an innovative computational approach to quantum mechanics. Over the course of this engaging and informal book, students are encouraged to take an active role in learning key concepts by working through practical exercises. The book equips readers with some basic methodology and a toolbox of scientific computing methods, so they can use code to simulate and directly visualize how quantum particles behave. The important foundational elements of the wave function and the Schrödinger equation are first introduced, then the text gradually builds up to advanced topics including relativistic, open, and non-Hermitian quantum physics. This book assumes familiarity with basic mathematics and numerical methods, and can be used to support a two-semester advanced undergraduate course. Source code and solutions for every book exercise involving numerical implementation are provided in Python and MATLAB®, along with supplementary data. Additional problems are provided online for instructor use with locked solutions.
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This concise textbook introduces an innovative computational approach to quantum mechanics. Over the course of this engaging and informal book, students are encouraged to take an active role in learning key concepts by working through practical exercises. The book equips readers with some basic methodology and a toolbox of scientific computing methods, so they can use code to simulate and directly visualize how quantum particles behave. The important foundational elements of the wave function and the Schrödinger equation are first introduced, then the text gradually builds up to advanced topics including relativistic, open, and non-Hermitian quantum physics. This book assumes familiarity with basic mathematics and numerical methods, and can be used to support a two-semester advanced undergraduate course. Source code and solutions for every book exercise involving numerical implementation are provided in Python and MATLAB®, along with supplementary data. Additional problems are provided online for instructor use with locked solutions.
This concise textbook introduces an innovative computational approach to quantum mechanics. Over the course of this engaging and informal book, students are encouraged to take an active role in learning key concepts by working through practical exercises. The book equips readers with some basic methodology and a toolbox of scientific computing methods, so they can use code to simulate and directly visualize how quantum particles behave. The important foundational elements of the wave function and the Schrödinger equation are first introduced, then the text gradually builds up to advanced topics including relativistic, open, and non-Hermitian quantum physics. This book assumes familiarity with basic mathematics and numerical methods, and can be used to support a two-semester advanced undergraduate course. Source code and solutions for every book exercise involving numerical implementation are provided in Python and MATLAB®, along with supplementary data. Additional problems are provided online for instructor use with locked solutions.
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