This page was generated from the Jupyter notebook compare_model_potentials.ipynb.

Compare different effective model potentials

import matplotlib.pyplot as plt

from ryd_numerov.rydberg import RydbergState

Check Rubidium with large n

For Rubidium and large quantum numbers n we expect the effective model potentials to be very similar.

state = RydbergState("Rb", n=40, l=0, j_tot=0.5)

states: dict[str, RydbergState] = {}


states["model_potential_marinescu_1993"] = RydbergState(state.species, n=state.n, l=state.l, j_tot=state.j_tot)
states["model_potential_marinescu_1993"].create_model(potential_type="model_potential_marinescu_1993")

states["model_potential_fei_2009"] = RydbergState(state.species, n=state.n, l=state.l, j_tot=state.j_tot)
states["model_potential_fei_2009"].create_model(potential_type="model_potential_fei_2009")

for label, state in states.items():
    print(f"Creating wavefunction for {label}")
    state.create_wavefunction()

Creating wavefunction for model_potential_marinescu_1993
Creating wavefunction for model_potential_fei_2009

fig, axs = plt.subplots(1, 2, figsize=(12, 6))

for ax in axs:
    linestyles = ["-", "--", "-.", ":"]
    for label, state in states.items():
        ax.plot(state.grid.z_list, state.wavefunction.w_list, label=label, lw=2, ls=linestyles.pop(0))

    ax.legend()
    ax.set_xlabel("$z$")
    ax.set_ylabel("$w(z)$")

axs[1].set_xlim(0, 5)

plt.show()

Big differences for Strontium with small n

state = RydbergState("Sr88", n=8, l=0, j_tot=0, s_tot=0)

states: dict[str, RydbergState] = {}


states["model_potential_marinescu_1993"] = RydbergState(
    state.species, n=state.n, l=state.l, j_tot=state.j_tot, s_tot=state.s_tot
)
states["model_potential_marinescu_1993"].create_model(potential_type="model_potential_marinescu_1993")

states["model_potential_fei_2009"] = RydbergState(
    state.species, n=state.n, l=state.l, j_tot=state.j_tot, s_tot=state.s_tot
)
states["model_potential_fei_2009"].create_model(potential_type="model_potential_fei_2009")

for label, state in states.items():
    print(f"Creating wavefunction for {label}")
    state.create_wavefunction()

The wavefunction for the state |Sr88:8,S_0⟩ has some issues:
      The wavefunction is not close to zero at the inner boundary (inner_weight_scaled_to_whole_grid=5.99e-01)
      The wavefunction has 3.0 nodes, but should have 7 nodes.
      The integration for l=0 did stop at 1.69 (should be close to zero).

Creating wavefunction for model_potential_marinescu_1993
Creating wavefunction for model_potential_fei_2009

fig, axs = plt.subplots(1, 2, figsize=(12, 6))

for ax in axs:
    linestyles = ["-", "--", "-.", ":"]
    for label, state in states.items():
        ax.plot(state.grid.z_list, state.wavefunction.w_list, label=label, lw=2, ls=linestyles.pop(0))

    ax.legend()
    ax.set_xlabel("$z$")
    ax.set_ylabel("$w(z)$")

axs[1].set_xlim(0, 5)

plt.show()