Double Delta Function Scattering Potential

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This Demonstration illustrates the transmission of a quantum-mechanical particle through a double delta function potential in one dimension. Multiple scattering between the two delta functions gives rise to resonances that depend on the spacing between the two delta functions as well as on the energy of the scattering particle.

Contributed by: Peter Falloon (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The one-dimensional double delta function potential, , is perhaps the simplest example of a scattering problem exhibiting the phenomenon of resonance. As the scattering wavefunctions can be found in closed form, it constitutes a very useful textbook-style example.

The resonance can be thought of as arising from interference between paths that are reflected a different number of times between the two barriers. In this Demonstration, both the energy of the incoming particle and the spacing between the two barriers can be varied.

Snapshot 1: lowest order resonance, corresponding to approximately half a wavelength between the two barriers

Snapshot 2: increasing the separation between the barriers decreases the energy of resonant transmission: here is the third resonance for a wider double barrier

Snapshot 3: bringing the barriers together destroys the resonance effect: here the barriers are very close together and the transmission function is very close to that of a single barrier



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