Using Mathematica for Quantum Mechanics: A Student's Manual

This book is an attempt to help students transform all of the concepts of quantum mechanics into concrete computer representations, which can be constructed, evaluated, analyzed, and hopefully understood at a deeper level than what is possible with more abstract representations.
Learning quantum mechanics is difficult and counter-intuitive. The first lectures I heard were filled with strange concepts that had no relationship with the mechanics I knew, and it took me years of solving research problems until I acquired even a semblance of understanding and intuition. This process is much like learning a new language, in which a solid mastery of the concepts and rules is required before new ideas and relationships can be expressed fluently.
The major difficulty in bridging the chasm between introductory quantum lectures, on the one hand, and advanced research topics, on the other, was for me the lack of such a language, or of a technical framework in which quantum ideas could be expressed and manipulated. On the one hand, I had the hand tools of algebraic notation, which are understandable but only serve to express very small systems and ideas; on the other hand I had diagrams, circuits, and quasi-phenomenological formulae that describe interesting research problems, but which are difficult to grasp with the mathematical detail I was looking for.
This book is an attempt to help students transform all of the concepts of quantum mechanics into concrete computer representations, which can be constructed, evaluated, analyzed, and hopefully understood at a deeper level than what is possible with more abstract representations. It was written for a Master’s and PhD lecture given yearly at the University of Basel, Switzerland. The goal is to give a language to the student in which to speak about quantum physics in more detail, and to start the student on a path of fluency in this language. We will revisit most of the problems encountered in introductory quantum mechanics, focusing on computer implementations for finding analytical as well as numerical solutions and their visualization.

Most of the calculations necessary to study and visualize such problems are too complicated to be done by hand. Even relatively simple problems, such as two interacting particles in a one-dimensional trap, do not have analytic solutions and require the use of computers for their solution and visualization. More complex problems scale exponentially with the number of degrees of freedom, and make the use of large computer simulations unavoidable.
The methods presented in this book do not pretend to solve large-scale quantum-mechanical problems in an efficient way; the focus here is more on developing a descriptive language. Once this language is established, it will provide the reader with the tools for understanding efficient large-scale calculations better.