Which Differential Equation Does a Finite Wave Train Follow?

[babblingsia]

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?

 

[pam]

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.

 

[lightarrow]

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.

 

[pam]

The normal wave equation has d^2/dt^2.

 

[lightarrow]

The normal wave equation has d^2/dt^2.

Yes, it's true.

 

[babblingsia]

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!

 

[pam]

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.