English | PDF | 2019 | 163 Pages | ISBN : N/A | 8.90 MB
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.
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