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LucKy
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- TL;DR Summary
- Question regarding unusual additional term added to the gaussian momentum distribution formula (used in computer simulation of 1D wavepacket scattering).
Hello everybody at the forum
I'm from Ukraine, I have Chemistry degree, and last year I began to self studying Quantum Mechanics.
I'm reading this article:
R. Garcia, A. Zozulya, and J. Stickney, “MATLAB codes for teaching quantum physics: Part 1,” [Online]. Available: http://arxiv.org/abs/0704.1622.
And I have a question about gaussian momentum distribution formula introduced in Program 6, section VII. WAVEPACKETS AND STEP POTENTIALS of the atticle.
The formula for gaussian momentum distribution (used in next steps to generate initial wave packet by Fourier Transform) in the above article is
## \phi(k) = e^{-a(k-k_0)^ 2}e^{-i6k^2}##
Please, can anybody expalain why the term ##e^{-i6k^2}## has been included into the wavepacket's gaussian momentum distribution frormula?
I have checked Townsend and Zettili books, but wavepacket's momentum distribution fromulas introduced in these books has no such term included.
When I modify the programm by deleting this term or by setting coefficient value less than 6, a second "mirror" wavepacket appears on a plot (and it moves in towards initial wavepacket).
I have two assumptions on this matter:
1) Adding this term is just a trick to run this particular computer simulation well, and there is no general need to include such term if I plan to use different algorithm or different calculation method for scattering simulation;
2) It is some type of "phase factor" for gaussian momentum distribution, and it was ommited in Townsend and Zettili books, but it is introduced in more advanced books. In this case, please give me advise where i can read about it;
I'm from Ukraine, I have Chemistry degree, and last year I began to self studying Quantum Mechanics.
I'm reading this article:
R. Garcia, A. Zozulya, and J. Stickney, “MATLAB codes for teaching quantum physics: Part 1,” [Online]. Available: http://arxiv.org/abs/0704.1622.
And I have a question about gaussian momentum distribution formula introduced in Program 6, section VII. WAVEPACKETS AND STEP POTENTIALS of the atticle.
The formula for gaussian momentum distribution (used in next steps to generate initial wave packet by Fourier Transform) in the above article is
## \phi(k) = e^{-a(k-k_0)^ 2}e^{-i6k^2}##
Please, can anybody expalain why the term ##e^{-i6k^2}## has been included into the wavepacket's gaussian momentum distribution frormula?
I have checked Townsend and Zettili books, but wavepacket's momentum distribution fromulas introduced in these books has no such term included.
When I modify the programm by deleting this term or by setting coefficient value less than 6, a second "mirror" wavepacket appears on a plot (and it moves in towards initial wavepacket).
I have two assumptions on this matter:
1) Adding this term is just a trick to run this particular computer simulation well, and there is no general need to include such term if I plan to use different algorithm or different calculation method for scattering simulation;
2) It is some type of "phase factor" for gaussian momentum distribution, and it was ommited in Townsend and Zettili books, but it is introduced in more advanced books. In this case, please give me advise where i can read about it;