How to Use NDSolve for Wave Pulse Propagation?

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SUMMARY

This discussion focuses on using NDSolve in Mathematica to numerically solve the time evolution of a one-dimensional wave pulse, specifically within the context of the time-dependent Schrödinger and Klein-Gordon equations. The primary challenge highlighted is the understanding of the necessary boundary and initial conditions required by NDSolve. A recommended resource for further reading is the book "Differential Equations with Mathematica" by Martha L. Abell and James P. Braselton, which includes a dedicated section on the wave equation.

PREREQUISITES
  • Familiarity with NDSolve in Mathematica
  • Understanding of one-dimensional wave equations
  • Knowledge of boundary and initial conditions in differential equations
  • Basic concepts of quantum mechanics related to the Schrödinger equation
NEXT STEPS
  • Read "Differential Equations with Mathematica" by Martha L. Abell and James P. Braselton
  • Explore the implementation of boundary conditions in NDSolve
  • Study the time-dependent Schrödinger equation and its applications
  • Investigate numerical methods for solving the Klein-Gordon equation
USEFUL FOR

Researchers, physicists, and students interested in computational physics, particularly those working with wave equations and numerical solutions in Mathematica.

FunkyDwarf
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Hey guys,

I'm sure I'm doing something really daft in not getting this to work, but...

I want to use NDSolve to numerically solve the time evolution of a (one-dimensional) wave pulse in either the time dependent Schrödinger or KG equations. My inability to do so stems from my lack of understanding of what boundary/initial conditions NDSolve wants/needs.

Essentially i'd like to just specify the initial form (gaussian or whatever) and a velocity and watch the thing fly off into the sunset, under what conditions will this occur?

Cheers
-G
 
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Dear, i think you have to read few pages from the following book,

"Differential equations with Mathematica" by Martha L. Abell and James P. Braselton.
there is a separate topic with deal with the wave equaiton
you can find it on gigapedia
 

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