Tutorial

This tutorial is made of notebooks that are available in the Siegpy/doc/notebooks folder after cloning the project. The aim of these series of notebooks is to present the most relevant capabilities offered by the SiegPy module while giving an overview of the Siegert states and how useful they can be in order to reproduce results obtained using the cumbersome continuum of states.

1D Square-Well Potential: the analytical case

First steps

• Find the Siegert and continuum states of a 1D Square-Well Potential case

Completeness relation in the 1D Square-well Potential case

• Completeness relation: an introduction
• Completeness relation: some problematic cases
• Completeness relation: a wider picture

Strength function

• Strength function: an introduction
• Strength function: convergence of the Mittag-Leffler expansion

Time propagation of a wavepacket

• Time propagation: an introduction
• Time propagation: wavepacket with an initial momentum
• Time propagation: error estimation of the Siegert states expansions

1D Square-Well Potential: the numerical case

Numerical bound and continuum states

• Numerical potential: bound and continuum states
• Completeness relation using numerical bound and continuum states

Numerical Siegert states

• Numerical potential: Siegert states
• Completeness relation with numerical Siegert states

Influence of some parameters on the numerical basis sets

• Virial operators
• Influence of the filters
• Influence of the coordinate mapping parameters: case study of the ErfKGCoordMap
• Influence of the grid for continuum states
• Influence of the grid for Siegert states

Other numerical potentials

• Symbolic Woods-Saxon potential
• Multiple Gaussian potentials
• Defining a new symbolic potential
• Strength function from numerical basis sets