# 2.7. Advanced onebody settings¶

We show some advanced settings for solving the onebody Schrödinger equation
which is based on Solving one-body problems.
In the following, `syst`

is a finalized kwant system with leads
and we import the onebody module from tkwant:

```
from tkwant import onebody
```

## 2.7.1. Boundary conditions¶

Special boundary conditions have to be provided in
order to solve the dynamic equations for an open quantum systems (with leads).
For `onebody.WaveFunction`

they must be precalculated:

```
boundaries = [tkwant.leads.SimpleBoundary(num_buffer_cells=500)] * len(syst.leads)
scattering_states = kwant.wave_function(syst, energy=1, params={'time':0})
lead, mode = 0, 0
psi_st = scattering_states(lead)[mode]
psi = onebody.WaveFunction.from_kwant(syst, psi_st, boundaries=boundaries, energy=1.)
```

For the scattering state solver boundary conditions are calculated on the fly.
One can provide different boundary conditions by the keyword `boundary`

```
boundaries = [tkwant.leads.SimpleBoundary(num_buffer_cells=500)] * len(syst.leads)
psi = onebody.ScatteringStates(syst, energy=1, lead=0, boundaries=boundaries)[mode]
```

For closed quantum systems (without leads), no boundary conditions are needed.

See also

A tutorial on boundary conditions is given in Boundary conditions. An example script which shows alternative boundary conditions is given in Alternative boundary conditions.

## 2.7.2. Time integration¶

The time integration can be changed by prebinding values with the module
`functool.partial`

to the onebody solver. In the current example, we
change the relative tolerance `rtol`

of the time-stepping algorithm:

```
import functools as ft
solver_type = ft.partial(tkwant.onebody.solvers.default, rtol=1E-5)
psi = onebody.WaveFunction.from_kwant(syst=syst, boundaries=boundaries,
psi_init=psi_st, energy=1.,
solver_type=solver_type)
```

## 2.7.3. Time-dependent perturbation¶

When the method `onebody.WaveFunction.from_kwant()`

is used,
the time-dependent perturbation \(W(t)\) is extracted from the Hamiltonian
of a Kwant system. By defaut, Tkwant uses cubic spline interpolation to interpolate
\(W(t)\) in time with a static discretization time \(dt\).
The interpolation is used for performance reasons,
in order to minimize the number of calls to Kwant.

One can change the discretization time \(dt\), which by default is \(dt = 1\), to a different value:

```
import functools as ft
perturbation_type = ft.partial(tkwant.onebody.kernels.PerturbationInterpolator, dt=0.5)
psi = onebody.WaveFunction.from_kwant(syst=syst, psi_init=psi_st, energy=1.,
boundaries=boundaries,
perturbation_type=perturbation_type)
```

Setting \(dt = 0\) will switch off interpolation and always evaluate the exact \(W(t)\) function. Alternatively, one can switch off interpolation directly with

```
psi = onebody.WaveFunction.from_kwant(syst=syst, psi_init=psi_st, energy=1.,
boundaries=boundaries,
perturbation_type=tkwant.onebody.kernels.PerturbationExtractor)
```

## 2.7.4. Saving and restarting states¶

Sometimes we might like to save a state in order to resume a calculation
on a later stage. An easy way is to to use the `pickle`

package:

```
import pickle
psi = onebody.WaveFunction.from_kwant(syst=syst, psi_init=psi_st, energy=1.,
boundaries=boundaries,
kernel_type=onebody.kernels.Scipy)
saved = pickle.dumps(psi)
```

Saving a state works currently only with the `tkwant.onebody.kernels.Scipy`

kernel.
The saved object `saved`

can be stored.
Recovering the state later on in order to continue the
calculation is possible by using

```
new_psi = pickle.loads(saved)
```

See Restarting calculations from previously saved results for the complete code.

See also

An example script showing the restarting of states is given in Restarting calculations from previously saved results.