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Determining quantum eigenfunctions in three-dimensional nanoscale structures
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10.1063/1.1896437
/content/aip/journal/jap/97/10/10.1063/1.1896437
http://aip.metastore.ingenta.com/content/aip/journal/jap/97/10/10.1063/1.1896437

Figures

Image of FIG. 1.
FIG. 1.

Diagram of the three-dimensional infinite well. The walls of the well are held at , which ensures that the wave form is reflected and contained in the problem space.

Image of FIG. 2.
FIG. 2.

Results of a simulation for a test function initiated at in Fig. 1. The top figure is the time-domain data. (Only the real part is displayed.) The bottom figure is the Fourier transform of the time-domain data. The eigenenergies corresponding to the peaks were identified at 775, 942, 1222, 1565, 1610, 1735, 2010, and .

Image of FIG. 3.
FIG. 3.

Results of a simulation for a test function initiated at in Fig. 1. New eigenenergies corresponding to the peaks at 1072, 1520, 2250, and were found.

Image of FIG. 4.
FIG. 4.

Diagram of an arbitrary quantum well. The shaded area represents zero potential while the surrounding area is . This structure was chosen to demonstrate the flexibility of the method because it cannot easily be analyzed. It does not correspond to any known practical device.

Image of FIG. 5.
FIG. 5.

Results of a simulation of the structure in Fig. 4 for a test function initiated at . The eigenenergies corresponding to peaks were found at 552, 762, 1150, 1530, 1830, 2162, 2560, and .

Image of FIG. 6.
FIG. 6.

Eigenfunctions corresponding to the first four eigenenergies found in Fig. 5.

Image of FIG. 7.
FIG. 7.

Vertical view ( plane) of the higher-energy eigenfunctions of Fig. 5.

Image of FIG. 8.
FIG. 8.

Time lapse of the eigenfunction. Notice that at the real and imaginary wave forms have evolved back to their original position, indicating a revival.

Image of FIG. 9.
FIG. 9.

A potential created by two positive point charges apart.

Image of FIG. 10.
FIG. 10.

Results of a simulation in the potential described by Fig. 9 for a test charge initiated at one of the points. The eigenenergies corresponding to peaks were found at and .

Image of FIG. 11.
FIG. 11.

Eigenfunctions corresponding to the eigenenergies found in Fig. 10.

Tables

Generic image for table
Table I.

The first 11 eigenenergies of the infinite three-dimensional potential well in Fig. 1. The analytic values were calculated from Eq. (7). The simulation values were determined from Figs. 2 and 3.

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/content/aip/journal/jap/97/10/10.1063/1.1896437
2005-05-02
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Determining quantum eigenfunctions in three-dimensional nanoscale structures
http://aip.metastore.ingenta.com/content/aip/journal/jap/97/10/10.1063/1.1896437
10.1063/1.1896437
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