Reference.Classes.wave

WavePacket main class "wave": Wavefunctions, represented on grids in position/momentum space

The classdef "wave" deals with wavefunctions and their representation in coordinate (position) space or in reciprocal (momentum) space using DVR|FBR methods. Quantum-mechanical observables are represented as (multiplicative and/or differential) operators, and the TDSE is represented as a partial differential equation. Because wavefunctions as well as operators are represented on multi-dimensional grids (direct|outer products of underlying one-dimensional grids), these simulations can become rather expensive. On a typical PC you cannot expect to treat problems with dimensionality exceeding 6.

Up until versions 4.x, the wavefunction picture was the only representation of quantum mechanics available within WavePacket, so that the functions (methods) of this classdef build on the oldest layers of the Matlab version of WavePacket which started in 2004. For the source codes of the classdef "wave" see here.

For an in-depth explanation of methods for solving the time-independent Schrödinger equation (TISE) in the wavefunction picture, see here.

For an in-depth explanation of methods for solving the time-dependent Schrödinger equation (TDSE) in the wavefunction picture, see here.

In addition to the methods that are required for each and every of the WavePacket main classes, the classdef "wave" contains the following public methods:

method	explanation	to be used when/where
diabatic	Transform initial wavefunction from adiabatic to diabatic representation	initial state only
eigen	Extract eigenfunctions from columns of eigenvector matrix of the Hamiltonian and normalize	bound states, see qm_bound
wigner	Wigner transform of a wavefunction	visualize 1-dim wavefunctions using contour or surface plots
normalize	Normalize (coupled) wavefunction(s)	calculation of eigenfunctions qm_bound and qm_propa
braket	Scalar product ⟨ f Ι g ⟩ of wave function and its Hermitian conjugate	calculate autocorrelation, see here
sandwich	Scalar product ⟨ f Ι O Ι g ⟩ with O being a multiplicative operator	calculations of matrix elements, see qm_matrix

Furthermore, the classdef "wave" contains the following public properties containing information about the matrices defining the state space (i.e. eigen) representation of the Hamiltonian, including coupling to external fields as well as to a thermal bath. This information is generated in qm_matrix and it is used in qm_abncd.

property	description
M_ham	Eigenenergies (vector)
M_dip	if applicable: dipole moments (matrix)
M_pol	if applicable: polarizability (matrix)
M_sbc	if applicable: system bath coupling (matrix)
M_amo	if applicable: additional multiplicative operators to be used as control targets
M_obs	choice of observables to be used as control targets: 'amo' or 'pop' or 'prj'
M_lab	labels for these observables (cell vector of text strings)