Which Differential Equation Does a Finite Wave Train Follow?

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In summary, the conversation discusses the properties of a finite wave train propagating along the positive x-axis with constant speed v. The question is raised whether the differential equation for this wave train must be the normal wave equation or the Schrodinger's equation. It is concluded that the normal wave equation is the correct one, as the shape of the wave remains unchanged. The Schrodinger's equation, on the other hand, involves derivatives that will cause the shape of the wave to change. The conversation also mentions that the Schrodinger's equation is more like the dispersion equation, due to its first-order in time.
  • #1
babblingsia
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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 Schrodinger's equation?
 
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  • #2
The normal wave train. The shape of f(x-vt) is unchanged in the wave equation.
Since the Schrodinger equation involves d^2/dx^2 and d/dt, the shape will change.
 
  • #3
pam said:
The normal wave train. The shape of f(x-vt) is unchanged in the wave equation.
Since the Schrodinger equation involves d^2/dx^2 and d/dt, the shape will change.
You have the same derivates in the normal wave equation.
 
  • #4
The normal wave equation has d^2/dt^2.
 
  • #5
pam said:
The normal wave equation has d^2/dt^2.
Yes, it's true.
 
  • #6
Ok so what if i haven't specified that the shape changes or not? I thought the schrodinger's eqn was like the universal wave equation of sorts!
 
  • #7
Because the Schrodinger equation is first order in time, it is more like the dispersion equation
(but with i d/dt) than the wave equation.
 

FAQ: Which Differential Equation Does a Finite Wave Train Follow?

What is a wave?

A wave is a disturbance that travels through a medium, transferring energy from one point to another without the physical transfer of matter.

What are the different types of waves?

There are three main types of waves: mechanical waves, electromagnetic waves, and matter waves. Mechanical waves require a medium to travel through, while electromagnetic waves can travel through a vacuum. Matter waves, also known as quantum waves, describe the wave-like behavior of particles at a quantum level.

How are waves formed?

Waves are formed when a source of energy, such as wind or vibration, causes a disturbance in a medium. This disturbance causes the particles in the medium to vibrate, creating a wave that travels outward from the source.

What is the difference between frequency and wavelength?

Frequency refers to the number of waves that pass a given point in a certain amount of time, usually measured in hertz (Hz). Wavelength, on the other hand, is the distance between two consecutive points on a wave that are in phase, or have the same amplitude and direction.

How are waves measured?

Waves can be measured in several ways, depending on the type of wave. For mechanical waves, the amplitude, frequency, and wavelength can be measured. Electromagnetic waves can be measured by their frequency or wavelength, and matter waves can be measured by their momentum or wavelength.

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