Using Mathematica for Quantum Mechanics

This book revisits many of the problems encountered in introductory quantum mechanics, focusing on computer implementations for finding and visualizing analytical and numerical solutions. It subsequently uses these implementations as building blocks to solve more complex problems, such as coherent laser-driven dynamics in the Rubidium hyperfine structure or the Rashba interaction of an electron moving in 2D. The simulations are highlighted using the programming language Mathematica. No prior knowledge of Mathematica is needed; alternatives, such as Matlab, Python, or Maple, can also be used.

Auteur
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.

Contenu

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 3.3.2magic 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 set 3.4.2asymptotic ground states 3.4.3Hamiltonian diagonalization 3.4.4analysis of the ground state 3.4.5exercises 4real-space systems 4.1one particle in one dimension 4.1.1computational basis functions 4.1.2example: square well with bottom step 4.1.3the Wigner quasi-probability distribution 4.1.41D dynamics in the square well 4.1.51D dynamics in a time-dependent potential 4.2non-linear Schrödinger equation 4.2.1ground state of the non-linear Schrödinger equation 4.3several particles in one dimension: interactions 4.3.1two identical particles in one dimension with contact interaction 4.3.2two particles in one dimension with arbitrary interaction 4.4one particle in several dimensions 4.4.1exercises 5combining space and spin 5.1one particle in 1D with spin 5.1.1separable Hamiltonian 5.1.2non-separable Hamiltonia...