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Easy to use Schrödinger equation solver

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# pyTALISES

**pyTALISES** (This Ain't a LInear Schrödinger Equation Solver) is an easy-to-use Python implementation of the Split-Step Fourier Method, for numeric calculation of a wave function's time-propagation under the Schrödinger equation.

### Features
- Calculation of a wavefunction's time propagation under a (non)linear Schrödinger equation: ![](https://latex.codecogs.com/png.latex?%5Cdpi%7B120%7D%20i%5Chbar%20%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial%20t%7D%20%5CPsi%20%28%5Cvec%7Br%7D%2C%20t%29%20%3D%20%5CBig%5BV%28%5CPsi%2C%5Cvec%7Br%7D%2C%20t%29%20&plus;%20%5Cfrac%7B%5Chbar%5E2%7D%7B2m%7D%5Cnabla%5E2%20%5CBig%5D%20%5CPsi%20%28%5Cvec%7Br%7D%2C%20t%29)
- the wave-function ![](https://latex.codecogs.com/gif.latex?%5Cdpi%7B100%7D%20%5CPsi) may include an arbitrary number of internal and external degrees of freedom
- simple implementation of Hamiltonians
- speed of the [FFTW](https://pypi.org/project/pyFFTW/), [BLAS](https://www.netlib.org/blas/) and [numexpr](https://numexpr.readthedocs.io/en/latest/) libraries with multithreading
- crucial functions are just-in-time compiled with [numba](https://numba.readthedocs.io/en/stable/)

### v2 API Quickstart

```python
import pytalises as pt

grid = pt.Grid(shape=(256,), extent=((-4, 4),))
psi = pt.Wavefunction(
    initial=["exp(-x**2)", "0"],
    grid=grid,
)

V = pt.HermitianPotential.from_lower_triangular([
    "0",
    "Omega*cos(t)",
    "Delta",
])

psi.propagate(
    potential=V,
    steps=1000,
    dt=1e-6,
    variables={"Omega": 2.0, "Delta": 1.0},
    options=pt.PropagationOptions(threads=4),
)
```

For migration details from the pre-v2 API, see `docs/source/v2_migration.rst`.

### Documentation
Read the [documentation](https://pytalises.readthedocs.io/en/latest/) to learn more about pytalises' capabilities.
The documentation features many examples, among others
[2D harmonic potentials](https://pytalises.readthedocs.io/en/latest/examples.html#2D-harmonic-potential), 
[BEC scattering](https://pytalises.readthedocs.io/en/latest/examples.html#Nonlinear-interactions-between-internal-states), 
[three-level Raman transitions](https://pytalises.readthedocs.io/en/latest/additional_examples.html#Three-level-Raman-transitions), 
[single-Bragg diffraction](https://pytalises.readthedocs.io/en/latest/additional_examples.html#Single-Bragg-diffraction) 
and
[atom interferometry](https://pytalises.readthedocs.io/en/latest/additional_examples.html#Light-pulse-atom-interferometry-with-single-Bragg-diffraction).

Installing pytalises
====================
**We recommend installing pytalises via conda**

pytalises supports Python 3.9 through 3.13, and wheels are built and tested across those versions in CI.

#### Using conda

Installing `pytalises` from the `conda-forge` channel can be achieved by adding `conda-forge` to your channels with:

```
conda config --add channels conda-forge
```

Once the `conda-forge` channel has been enabled, `pytalises` can be installed with:

```
conda install pytalises
```

#### Using pip

pytalises is available on the Python Package Index and can be installed via

```
pip install pytalises
```

it has dependencies via `scipy` and `numba` on BLAS and LAPACK libraries that are not always found on windows systems. For linux they can usually be located.

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