Numerics.Main

WavePacket background: Physics & Numerics

In order to solve Schrödinger's equations, as well as classical, quantum classical and quantum Liouville equations in an efficient and accurate manner, WavePacket has a set of numerical standard techniques built-in. Being very versatile, it allows for a choice of various Hamiltonian operators, different initial states as well as different boundary conditions. Moreover, WavePacket can also be used to solve sets of coupled(!) Schrödinger or Liouville equations occuring for problems featuring fast and slow degrees of freedom (or light and heavy particles). In particular, it allows to simulate non-adiabatic transitions of heavy particles' wavefunctions occurring predominantly at (avoided) crossings or (conical) intersections of light particles' eigenenergy hypersurfaces.

• Schrödinger's equations and Hamiltonians
• Discrete variable representations
  • Fourier grid representations and absorbing boundary conditions
• Solving the time-independent Schrödinger equation
• Solving the time-dependent Schrödinger equation
  • Choosing time steps and truncating the Hamiltonian
• Solving the classical Liouville equation
• Solving the quantum-classical Liouville equation
• Solving the Liouville-von Neumann equation
• Setting up a thermal initial state
• Controlling quantum dynamics by external fields
• Optimal control theory in quantum dynamics
• Dimension reduction in control systems
• Atomic units

Detailed descriptions can also be found in our articles describing the Matlab/Octave version of WavePacket