Visualizing electron wave motion: solving the time-dependent Schroedinger equation

Visualizing electron wave motion: solving the time-dependent Schroedinger equation

Visualizing electron wave motion in quantum nano-devices

see also: scientific work and software development by Gerhard Fasol

We simulate quantum devices by solving the time-dependent Schroedinger equation. We apply our software for a variety of problems. Our simulations can be used for simulating electrons in electron microscopes and for simulating electronic devices using quantum effects. Another area is the simulation of electron wave packets prepared by femto-second laser pulses. Femto-second laser technology is a very rapidly growing area, and it is very difficult to imagine how electron wave packets behave on such a short time scale without high quality simulations. Our software can also be used for a range of other simulation technology applications.

Visualizing electron wave motion Prize in the Japanese Computer Visualization Contest

This work has been awarded the 2nd Prize in the Japanese Computer Visualization Contest 1995 organized by the Japanese Edition of Scientific American (Nikkei SCIENCE) (優秀賞「KGT賞」『極小・超高速半導体デバイスを設計するための量子輸送シミュレーション』), it has also appeared on the February 1996 page of the Hewlett-Packard Laboratory Calender, and the work has also been presented at a number of scientific conferences and in a number of scientific journals. We have also presented the first simulation of electrons in strong magnetic fields at the 23rd Conference on The Physics of Semiconductors on Berlin (1996), and at a number of Japanese Applied Physics and Engineering conferences and scientific publications. Simulation results were also presented on the New Year cards of the Institute of Industrial Science of the University of Tokyo.

In the next few slides we show you an electron wave moving through the potential landscape shown in the next image below.

Potential landscape simulates an electron beam diffracted by a thin crystal slab

Potential landscape used for this simulation
Potential landscape for this demonstration: an electron wave packet emerges from the channel on the left. The wave packet then propagates through a thin periodic lattice. This lattice could represent the atoms in a crystal for example.

Snapshot of the real part of the electron wave function 25 femtoseconds after start of simulation

real part of the electron wave function 25 femtoseconds after the simulation started
This slide shows the real part of the electron wave function 25 femtoseconds after the simulation started. The figure shows that plane electron waves emerge in particular directions, these are the directions where Bragg peaks occur. The next slide will show the corresponding electron probability density.

Snapshot of the electron probability density derived from the electron wave function 25 femtoseconds after start of simulation

electron probability density derived from the electron wave function 25 femtoseconds after the simulation started
This slide shows the electron probability density derived from the electron wave function 25 femtoseconds after the simulation started.
The next slide will show an animation of the wave function.

Movie showing the evolution of the real part of the wave function during the scattering process

real part of the electron wave function propagating through a periodic potential
This slide shows the real part of the electron wave function propagating through a periodic potential shown in the first slide of this series.
This slide (and the next) will show animations of the wave function.

Movie showing the evolution of the probability density during the scattering process

Probability density of electron wave scattered by the potential modeling a very thin crystal
This slide shows the probability density of the electron wave function propagating through a periodic potential shown in the first slide of this series.
This slide shows animations of the wave function.

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