Compute vibrational levels, wavefunctions, and expectation values using the Numerov-Cooley algorithm.
Copyright and license
Copyright 2017 Radovan Bast. Use of this source code is governed by a the Mozilla Public License v2.0 that can be found in the LICENSE file.
If you use this tool in a program or publication, please acknowledge its author(s) by adding the following reference:
- Numerov 0.5.0, October 2017, Radovan Bast, UiT The Arctic University of Norway, Norway, https://doi.org/10.5281/zenodo.1000406.
pip install numerov
Please have a look here.
This script will calculate the vibrational levels (and wavefunctions) corresponding to a normal mode numerically using the Numerov-Cooley algorithm.
The script will increase the energy and count the nodes of the wave function.
If the number of nodes changes and stepsize is below
energy_precision_hartree, it will
accept the solution, integrate the property along q and move on to the next
num_solutions is reached. It will also calculate the transition
frequencies 0 -> n, this is useful to check against the harmonic frequencies.
energy_precision_hartreeis often more important than number of grid points.
- Be careful with the displacement range.
- If the script enters an endless loop probably the reduced mass or the displacement range is wrong.
- Practice first with the harmonic oscillator.
- It is a good idea to play with parameters to check convergence and numerical stability.
- Potential and property are approximated by polynomials that contain coefficients FROM ZEROTH to nth order (that's what polyfit gives) and you might not want that (for instance you might insist that the gradient of the potential is zero at equilibrium) in this case you can provide your own expansion coefficients or program an alternative interpolation scheme.