Is Wave Phenomena Related to PDE or Just Physics?

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SUMMARY

Wave phenomena are intrinsically linked to Partial Differential Equations (PDE), particularly through dispersive wave equations such as the Schrödinger wave equation. These equations are analyzed qualitatively to determine the propagation of solutions over time. While wave phenomena are often studied in physics, they are fundamentally described using PDEs, establishing a clear connection between the two fields.

PREREQUISITES
  • Understanding of Partial Differential Equations (PDE)
  • Familiarity with dispersive wave equations
  • Basic knowledge of quantum mechanics, specifically the Schrödinger wave equation
  • Foundational concepts in wave physics
NEXT STEPS
  • Explore the properties of dispersive wave equations in detail
  • Study the qualitative analysis of PDE solutions
  • Investigate the applications of the Schrödinger wave equation in quantum mechanics
  • Learn about wave phenomena in various physics contexts, including classical and modern physics
USEFUL FOR

Students and professionals in mathematics, physics, and engineering, particularly those interested in the intersection of wave phenomena and Partial Differential Equations.

mathmari
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Hey! :o

Do you know if "Wave Phenomena" are related to PDE or only to physics?? (Wondering)
 
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mathmari said:
Hey! :o

Do you know if "Wave Phenomena" are related to PDE or only to physics?? (Wondering)

There is a large class of PDE known as dispersive wave equations. These equations are usually studied qualitatively. For example, one seeks to determine if solutions propagate in finite time or if they exist globally. If you've studied quantum mechanics, then you've seen a dispersive equation -- the Schrödinger wave equation.
 
Euge said:
There is a large class of PDE known as dispersive wave equations. These equations are usually studied qualitatively. For example, one seeks to determine if solutions propagate in finite time or if they exist globally. If you've studied quantum mechanics, then you've seen a dispersive equation -- the Schrödinger wave equation.

Ok! Thank you for the information! (Yes)
 
I would definitely say that wave phenomena are definitely related to both fields. Waves are described using PDE's, so they're related to that field; on the other hand, you usually study waves as a separate topic in most first-year physics courses, as well as more advanced physics courses where you actually solve the PDE.
 

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