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Transmission resonances and Bloch states for a periodic array of delta function potentials
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10.1119/1.4769113
/content/aapt/journal/ajp/81/3/10.1119/1.4769113
http://aip.metastore.ingenta.com/content/aapt/journal/ajp/81/3/10.1119/1.4769113

Figures

Image of Fig. 1.
Fig. 1.

(a) A finite array of six delta-function potentials on a line. (b) A periodic array of six delta-function potentials on a ring.

Image of Fig. 2.
Fig. 2.

Transmission coefficient as a function of energy for an evenly spaced array of 10 delta functions with

Image of Fig. 3.
Fig. 3.

Detailed plot of the first “band” of the transmission coefficient in Fig. 2 .

Image of Fig. 4.
Fig. 4.

Real part of the transmission amplitude as a function of energy in the first “band” of an equally spaced array of 10 delta functions with

Image of Fig. 5.
Fig. 5.

Unnormalized transmission resonance wave functions in the lowest energy band for N = 3, 4, and 5, assuming the delta functions act as impenetrable barriers. The abscissa labels correspond to the positions of the first and last delta-function potentials in the chains. The maximum amplitude is arbitrarily taken equal to 1.

Image of Fig. 6.
Fig. 6.

(Color online) Real (dashed curves) and imaginary (solid curves) parts of the unnormalized wave function at the transmission resonances for and N = 5. The real part of the wave function is multiplied by a factor of 10 for visibility. The abscissa labels correspond to the positions of the first and last delta function potentials in the chains.

Image of Fig. 7.
Fig. 7.

(Color online) Real (dashed curves) and imaginary (solid curves) parts of the unnormalized wave function at the transmission resonances for and N = 6. The real part of the wave function is multiplied by a factor of 10 for visibility. The abscissa labels correspond to the positions of the first and last delta function potentials in the chains.

Image of Fig. 8.
Fig. 8.

Unnormalized probability distribution for the lowest-energy transmission resonances in each of the first three energy bands for and N = 6. The abscissa labels correspond to the positions of the first and last delta function potentials in the chains.

Image of Fig. 9.
Fig. 9.

(Color online) Real (solid curves) and imaginary (dashed curves) parts of the normalized Bloch-state wave functions for and N = 5. The delta-function potentials are located at half-integral positions on the ring.

Image of Fig. 10.
Fig. 10.

(Color online) Real (solid curves) and imaginary (dashed curves) parts of the normalized Bloch-state wave functions for and N = 6. The delta-function potentials are located at half-integral positions on the ring.

Image of Fig. 11.
Fig. 11.

(Color online) Real (solid curves) and imaginary (dashed curves) parts of the periodic functions for and N = 6, along with the corresponding probability distributions .

Image of Fig. 12.
Fig. 12.

(Color online) Graphs of for the Bloch states as a function of the delta-function potential strength parameter . For , the values of correspond to those of a free particle constrained to move on a ring, but with increasing , the band structure emerges. Solid (red) curves correspond to doubly degenerate states and dashed (blue) curves to nondegenerate states.

Tables

Generic image for table
Table I.

Values for the transmission and Bloch state energies for .

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/content/aapt/journal/ajp/81/3/10.1119/1.4769113
2013-02-19
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Transmission resonances and Bloch states for a periodic array of delta function potentials
http://aip.metastore.ingenta.com/content/aapt/journal/ajp/81/3/10.1119/1.4769113
10.1119/1.4769113
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