H2+ IN THE BORN OPPENHEIMER APPROXIMATION
===============================================

by Sigurd Askeland (sigurd.askeland@gmail.com)


This software package contains programs for solving the Schrödinger equation
for H2+ in a laser field, within the Born Oppenheimer approximation. 

The electronic part of the problem is solved using a prolate spheroidal 
coordinate system. The time independent electronic problem is solved 
using a basis function representation. This is described in detail in the 
article 'Kamta and Bandrauk, Phys. Rev. A 71, 053407 (2005)'. 
The time dependent part is solved in the eigenstate basis.

The vibrational part of the problem is solved using a B-spline basis.
See the article 
    "H. Bachau et al. 'Applications of B-splines in atomic and 
    molecular physics.', Rep. Prog. Phys., 64:1815-1943, 2001."

The code is parallelized, and in well documented python.
Feel free to copy and change the code. If you make improvements, I would 
appreciate a copy of the relevant code.


Here comes an overview of some of the constituents of the software package,
those used to set ut the Hamiltonian matrix and the basis functions.

Main program
============
main.py : insert all problem parameters here, and press play*. Calls upon the 
    programs listed below. The result is the full Hamiltonian and overlap matrices,
    stored to HDF5 files, as well as the eigenstates and energies for analysis.
    
    * play means: 
    $ mpirun -n 20 python main.py

Electronic part
===============
electronic_BO.py : the main program for solving the electronic time 
    independent Schrödinger equation (TISE) for multiple internuclear 
    distances. Parallelized.

tdse_electron.py : the main program for calculating the dipole couplings for
    multiple internuclear distances. Parallelized.

--- The two programs above call on the rest of them.

tise_electron.py : sets up the TISE hamiltonian matrix, solves the eigenvalue 
    problem, and stores the results to file.

psc_basis.py : sets up the prolate spheroidal coordinate basis, including the 
    overlap matrix.

config.py : class for containing the parameters that uniquely define a basis.

index_iterator.py : class for looping over basis functions.

gausslaguerrequadrature.py : class for solving the 'radial' integrals, or more
    precisely, the integrals in the 'xi' variable.


Vibrational part
================
vibrational_BO.py : the main program for calculating the vibrational 
    eigenstates, as well as the Hamiltonian matrix for the full time dependent
    H2+ Schrödinger equation. Parallelized.

--- The program above calls the programs below.

vibrational_methods.py : sets up the basis, and calculates and saves the 
    hamiltonian matrices.

bsplines.py : contains all the good stuff for a B-spline basis.

breakpointsequences.py : support program for bsplines.

gausslegendrequadrature.py : class for solving the integrals in the B-spline 
    basis.


General
=======
name_generator.py : assures consistent naming of ... anything, really.

nice_stuff.py : contains misc. small functions that are often useful. 


Debugging tools
===============
--- These programs are poorly documented, and may be of use only to me.
test_tdse_electron.py 
test_tise_electron.py 
test_psc_basis.py 
test_vibrational_methods.py


Documentation
=============
A_6.pdf : shows the steps needed from eq. (A6) in Kamta2005 to implementation.
A_6.tex : shows the steps needed from eq. (A6) in Kamta2005 to implementation.


Propagation
===========
Directory containing programs for propagating the Schrödinger Equation.


Fortran_propagation
===================
Directory containing programs for propagating the Schrödinger Equation fast and
in parallel for large H2+ problems.

Analysis
========
Directory containing programs for analyzing the results of the propagation.