1 Wolfram language overview
1.1 introduction
1.1.1 exercises
1.2 variables and assignments
1.2.1 immediate and delayed assignments
1.2.2 exercises
1.3 four kinds of bracketing
1.4 prefix and postfix
1.4.1 exercises
1.5 programming constructs
1.5.1 procedural programming
1.5.2 exercises
1.5.3 functional programming
1.5.4 exercises
1.6 function definitions
1.6.1 immediate function definitions
1.6.2 delayed function definitions
1.6.3 functions that remember their results
1.6.4 functions with conditions on their arguments
1.6.5 functions with optional arguments
1.7 rules and replacements
1.7.1 immediate and delayed rules
1.7.2 repeated rule replacement
1.8 many ways to define the factorial function
1.8.1 exercises
1.9 vectors, matrices, tensors
1.9.1 vectors
1.9.2 matrices
1.9.3 sparse vectors and matrices
1.9.4 matrix diagonalization
1.9.5 tensor operations
1.9.6 exercises
1.10 complex numbers
1.11 units
2 quantum mechanics
2.1 basis sets and representations
2.1.1 incomplete basis sets
2.1.2 exercises
2.2 time-independent Schrödinger equation
2.2.1 diagonalization
2.2.2 exercises
2.3 time-dependent Schrödinger equation
2.3.1 time-independent basis
2.3.2 time-dependent basis: interaction picture
2.3.3 special case: I ˆ(t), ˆ(tt)l = 0 ?(t, tt)
H H
2.3.4 special case: time-independent Hamiltonian
2.3.5 exercises
2.4 basis construction
2.4.1 description of a single degree of freedom
2.4.2 description of coupled degrees of freedom
2.4.3 reduced density matrices
2.4.4 exercises
3 spin systems
3.1 quantum-mechanical spin and angular momentum operators
3.1.1 exercises
3.2 spin-1/2 electron in a dc magnetic field
3.2.1 time-independent Schrödinger equation
3.2.2 exercises
3.3 coupled spin systems: 87Rb hyperfine structure
3.3.1 eigenstate analysis
3.3.2 “magic” magnetic field
3.3.3 coupling to an oscillating magnetic field
3.3.4 exercises
3.4 coupled spin systems: Ising model in a transverse field
3.4.1 basis set
3.4.2 asymptotic ground states
3.4.3 Hamiltonian diagonalization
3.4.4 analysis of the ground state
3.4.5 exercises
4 real-space systems
4.1 one particle in one dimension
4.1.1 computational basis functions
4.1.2 example: square well with bottom step
4.1.3 the Wigner quasi-probability distribution
4.1.4 1D dynamics in the square well
4.1.5 1D dynamics in a time-dependent potential
4.2 non-linear Schrödinger equation
4.2.1 ground state of the non-linear Schrödinger equation
4.3 several particles in one dimension: interactions
4.3.1 two identical particles in one dimension with contact interaction
4.3.2 two particles in one dimension with arbitrary interaction
4.4 one particle in several dimensions
4.4.1 exercises
5 combining space and spin
5.1 one particle in 1D with spin
5.1.1 separable Hamiltonian
5.1.2 non-separable Hamiltonian
5.1.3 exercises
5.2 one particle in 2D with spin: Rashba coupling
5.2.1 exercises
5.3 phase-space dynamics in the Jaynes–Cummings model
exercises
