Using Mathematica for Quantum Mechanics

1Wolfram language overview1.1introduction1.1.1exercises1.2variables and assignments1.2.1immediate and delayed assignments1.2.2exercises1.3four kinds of bracketing1.4prefix and postfix1.4.1exercises1.5programming constructs1.5.1procedural programming1.5.2exercises1.5.3functional programming1.5.4exercises1.6function definitions1.6.1immediate function definitions1.6.2delayed function definitions1.6.3functions that remember their results1.6.4functions with conditions on their arguments1.6.5functions with optional arguments1.7rules and replacements1.7.1immediate and delayed rules1.7.2repeated rule replacement1.8many ways to define the factorial function1.8.1exercises1.9vectors, matrices, tensors1.9.1vectors1.9.2matrices1.9.3sparse vectors and matrices1.9.4matrix diagonalization1.9.5tensor operations1.9.6exercises1.10complex numbers1.11units2quantum  mechanics 2.1basis sets and representations 2.1.1incomplete basis sets 2.1.2exercises 2.2time-independent Schrödinger equation 2.2.1diagonalization 2.2.2exercises 2.3time-dependent Schrödinger equation 2.3.1time-independent  basis 2.3.2time-dependent basis: interaction picture 2.3.3special case: I (t), (tt)l = 0 (t, tt) HH2.3.4special case: time-independent Hamiltonian 2.3.5exercises 2.4basis construction 2.4.1description of a single degree of freedom 2.4.2description of coupled degrees of freedom 2.4.3reduced density matrices 2.4.4exercises 3spin systems 3.1quantum-mechanical spin and angular momentum operators 3.1.1exercises 3.2spin-1/2 electron in a dc magnetic field 3.2.1time-independent Schrödinger equation 3.2.2exercises 3.3coupled spin systems: 87Rb hyperfine structure 3.3.1eigenstate analysis 3.3.2"magic" magnetic field 3.3.3coupling to an oscillating magnetic field 3.3.4exercises 3.4coupled spin systems: Ising model in a transverse field 3.4.1basis

PD Dr. Roman Schmied studied physics at the École Polytechnique Fédérale de Lausanne and the University of Texas at Austin. He wrote his diploma thesis on helium nanodroplet spectroscopy at Princeton University with Kevin Lehmann and Giacinto Scoles, and later obtained his Ph.D. from the same group, working on the superfluidity of helium nanodroplets and on the spectroscopy of molecules solvated within these droplets. He carried out his postdoctoral work at the Max Planck Institute of Quantum Optics in Garching, Germany, where he first began working with quantum simulators and quantum simulations. After a short stay at the NIST ion storage group in Boulder, USA, he took on his current position at the University of Basel, where he was habilitated in 2017. Since 2016 he has also been working at the University's Human Optics Lab, where he is currently using digital technology for child health, particularly eye health.