Which Differential Equation Does a Finite Wave Train Follow?

  • Context: Graduate 
  • Thread starter Thread starter babblingsia
  • Start date Start date
  • Tags Tags
    Waves
Click For Summary

Discussion Overview

The discussion centers on the differential equations governing the propagation of a finite wave train, specifically whether it must satisfy the normal wave equation or the Schrödinger equation. The scope includes theoretical considerations of wave behavior and the mathematical properties of these equations.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant proposes that a finite wave train propagating with constant speed v without changing shape must satisfy the normal wave equation.
  • Another participant argues that the normal wave equation preserves the shape of f(x-vt), while the Schrödinger equation, which involves second derivatives in space and first derivatives in time, leads to changes in shape.
  • A subsequent post reiterates the point about the normal wave equation maintaining the shape of f(x-vt) and emphasizes the presence of similar derivatives in both equations.
  • Another participant notes that the normal wave equation includes a second time derivative, d^2/dt^2.
  • One participant questions the implications of not specifying whether the shape changes, suggesting that the Schrödinger equation might be viewed as a universal wave equation.
  • Another participant clarifies that the Schrödinger equation is first order in time and likens it more to a dispersion equation rather than a wave equation.

Areas of Agreement / Disagreement

Participants express differing views on whether the finite wave train must follow the normal wave equation or the Schrödinger equation, with no consensus reached on the matter.

Contextual Notes

Participants have not specified assumptions regarding the nature of the wave train or the conditions under which the equations apply, leaving some aspects of the discussion unresolved.

babblingsia
Messages
9
Reaction score
0
Suppose I have a FINITE wave train, ( of an unspecified nature), and it propagates along say the positive x-axis with a constant speed v and without any change of shape. Now which differential equation it MUST satisfy? The normal wave equation or the Schrödinger's equation?
 
Physics news on Phys.org
The normal wave train. The shape of f(x-vt) is unchanged in the wave equation.
Since the Schrödinger equation involves d^2/dx^2 and d/dt, the shape will change.
 
pam said:
The normal wave train. The shape of f(x-vt) is unchanged in the wave equation.
Since the Schrödinger equation involves d^2/dx^2 and d/dt, the shape will change.
You have the same derivates in the normal wave equation.
 
The normal wave equation has d^2/dt^2.
 
pam said:
The normal wave equation has d^2/dt^2.
Yes, it's true.
 
Ok so what if i haven't specified that the shape changes or not? I thought the Schrödinger's eqn was like the universal wave equation of sorts!
 
Because the Schrödinger equation is first order in time, it is more like the dispersion equation
(but with i d/dt) than the wave equation.
 

Similar threads

Graduate Schrödinger's equation: a diffusion or a wave equation?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad The wave equation interpretation of special relativity
  • · Replies 10 ·
Replies
10
Views
1K
Graduate Electric and magnetic field lines in a plane wave of finite extent
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Differentiated Sakharov Equation for Vacuum Fluctuations
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad How do you normalize this wave function?
  • · Replies 31 ·
2
Replies
31
Views
6K
Undergrad Understanding Gauge Symmetry: A Review of the Schrödinger Equation
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Dispersion Relation in Different Media
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Why does the Dirac equation lead to spin 1/2?
  • · Replies 8 ·
Replies
8
Views
8K
Time it Takes for a Transverse Pulse to Travel a Distance "L" Up a Cable Against Gravity?
  • · Replies 13 ·
Replies
13
Views
2K
Graduate Physical meaning of a wave packet w/ respect to HUP&duality
  • · Replies 6 ·
Replies
6
Views
2K