We have performed quantum mechanical probability current calculations through a simple two dimensional (2D) jellium potential modeling the STM tip - nanotube - support system. STM constant current feedback loop was simulated by moving the tip along a line (''quantum line cut'' ) where the transferred probability was constant.

The 2D model potential has
the value *zero* outside the effective surfaces
of the electrodes and the value inside.
( , ).

Tunneling probability is calculated from time dependent
scattering of a Gaussian wave packet approaching the model
potential from the bulk of the tip.
The probability current density was calculated along a horizontal
line inside the support bulk (at ).
Line integration of along this line gives the
*I*(*t*) probability current and the tunneling probability is
obtained as .

Probability density of the scattered wave packet is shown on
*Fig. 6.*.

**Figure 6:**
Probability density of scattered wave packet for
selected time instants and for selected *X*_{apex} lateral
tip displacements.
Effective surfaces of electrodes are shown by red lines.
Size of presentation window is
.
Contour lines are drawn on sqare root scale.
Each frame is normalized to its maximum density.
Initial momentum of Gaussian wave packet is
and its initial with is
.

- For the tip is far from the nanotube. Wave packet is tunneling simply from the tip apex into to plane support.
- For tip is above the uppermost point of nanotube. It is a resonant tunneling situation. The probability which remained in the tube region forms standing waves and is leaking into the tip and into the support in distinct impulses[6].
- For (oblique incidence) majority of the probability flows out of the tip at its side around the nearest points of the sample and tip.
- For we can observe switching of the tunneling points.

X_{apex} (nm) |
Forbidden | Tube | Total Interface = Forbidden + Tube |

0.0 | 0.071 | 0.084 | 0.155 |

0.8 | 0.079 | 0.123 | 0.202 |

1.6 | 0.060 | 0.020 | 0.080 |

2.0 | 0.057 | 0.0001 | 0.057 |

STM constant current loop was simulated by finding for each fixed

**Figure 7:**
Comparison of geometric and quantum line cut.
Thick red line is the geometric line cut.
Crosses show calculated points of quantum line cut.