Gaussian Wavepacket Tunnel Through double barrier

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Discussion Overview

The discussion revolves around creating a movie in Matlab that simulates a Gaussian wave packet interacting with a double barrier. Participants are seeking and providing assistance on how to implement this simulation, including coding techniques and mathematical approaches.

Discussion Character

  • Homework-related
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant requests help with Matlab code for simulating a Gaussian wave packet moving towards a double barrier.
  • Another participant suggests using a for loop with the plot command to animate the Gaussian wave packet and mentions the pause command for timing between frames.
  • A third participant recommends checking the 'help movie' command to collect plots as movie frames and adjust playback settings.
  • One participant expresses gratitude for the advice but indicates difficulty in implementing the Gaussian wave packet mathematically in Matlab.
  • Another participant proposes using a Runge-Kutta algorithm for handling integrals related to the simulation, while noting their lack of experience with coding a Gaussian wave packet.
  • A different participant suggests that a split-operator FFT method may be more efficient than direct integral solutions for this type of problem.
  • One participant questions whether modeling the Gaussian wave packet as a superposition of component frequencies is necessary, suggesting that a simpler approach using a monochromatic beam with a Gaussian envelope might suffice for the animation.

Areas of Agreement / Disagreement

Participants present various methods and approaches to simulate the Gaussian wave packet, but there is no consensus on the best method to implement. Some suggest more complex techniques while others advocate for simpler solutions.

Contextual Notes

There are unresolved mathematical steps regarding the implementation of the Gaussian wave packet in Matlab, and participants express uncertainty about the necessity of complex modeling techniques.

mehdikhann
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Hello,
I was trying to design a movie in Matlab. A Gaussian wave packet moves toward double barrier then some wave reflect and some pass out from the barrier . i design the double barrier in Matlab. but don't know how to make movie in Matlab with Gaussian wavepacket. can you help. Do u have the code in Matlab
 
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mehdikhann said:
Hello,
I was trying to design a movie in Matlab. A Gaussian wave packet moves toward double barrier then some wave reflect and some pass out from the barrier . i design the double barrier in Matlab. but don't know how to make movie in Matlab with Gaussian wavepacket. can you help. Do u have the code in Matlab

There is a programming subforum down below.

Short answer: the plot command in a for loop. You plot your function (the gaussian wave packet) and then compute the new shape of the function every time through the for loop, and then plot it.

You can use the pause command (type help pause) to put time between your frame changes.
 
also check out 'help movie'. You can collect each of your plots as a movie frame and build a movie out of it, then once you have the movie array, you can adjust the frame-rate and the number of plays as you want.
 
Hej Pythoagorean,
Thankyou very much for reply. i use the movie frame and it work for some equation. but i was trying move to gaussian wave packet but don't know how implement on MATLAB mathematically . do u have code for Gaussian wave packet
 
Here's the general analytic structure:

http://musr.physics.ubc.ca/~jess/hr/skept/GWP/

Shooting from the hip, I'd use a runge-kutta algorithm to handle the integral, but you may want to see if there's some more experienced replies. I've never coded a gaussian wave packet before.
 
Last edited by a moderator:
A split-operator FFT metthod is usually more efficient than solving the integral directly for these kinds of problems.
You should be able to find a description of this method in just about any book on computational physics.
 
If I'm understanding these suggestions correctly, then what is being advised is to model the Gaussian wave packet as the superposition of its component frequencies. While this is certainly correct, it's probably overkill for the animation in question. I'm pretty sure you'll get almost the identical picture simply by calculating the reflection/transmission of a monochromatic beam and then just putting a Gaussian envelope over it.
 

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