  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. On our journey we approach questions such as: -- You already know how
to calculate the energy eigenstates of a single particle in a simple
one-dimensional potential. How can such calculations be generalized to
non-trivial potentials, higher dimensions, and interacting particles? -- You
have heard that quantum mechanics describes our everyday world just as well as
classical mechanics does, but have you ever seen an example where such behavior
is calculated in detail and where the transition from classical to quantum
physics is evident? -- How can we describe the internal spin structure of
particles? How does this internal structure couple to the particles' motion? --
What are qubits and quantum circuits, and how can they be assembled to simulate
a future quantum computer?
