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Mathematical Background
Vector Spaces and Linear Operators
Vector Spaces and Basic Properties
Normed, Inner Product and Complete Vector Space
Linear Operators
Hilbert Spaces and Quantum States
Spectral Theory in Hilbert Spaces
Self-adjoint Operators and Observables
Spectral Decomposition in Infinite Dimensions
Functions of Observables and Time Evolution
Adiabatic vs Diabatic Representation
Born--Oppenheimer Separation
Adiabatic Representation
Diabatic Representation
Adiabatic Transform
Time Evolution in Quantum Mechanics
Numerical Schemes for TDSE
Split-Operator Method
Crank--Nicolson Scheme
Imaginary Time Propagation
Holy Trinity of Variational Principles
Dirac--Frenkel Principle
McLachlan's Variational Principle
Time-Dependent Variational Principle
Mixed Quantum-Classical Dynamics
Quantum Amplitude Propagation in Mixed Schemes
The Time Derivative Coupling
The Hammes-Schiffer Tully Scheme
The Norm-Preserving Interpolation
The Baeck--An Scheme
Ehrenfest Dynamics
Fewest Switches Surface Hopping
Landau--Zener Surface Hopping
Mapping Approach to Surface Hopping
Beyond Surface Hopping
Source Code
Code Documentation
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