What is the menaing of standing plane waves ?

In summary, standing plane waves are waves that do not propagate but appear to stand still. In the context of quantum mechanics, they are necessary for practical boundary conditions and can be described by a mathematical function such as \psi(x, y, z, t) = A \cos (kz) \exp (i \omega t). The use of "standing" emphasizes the stationary nature of the waves.
  • #1
skarthikselvan
5
0
What is the menaing of "standing plane waves"?

Hi All,

For me, English is my second language and I am not good is waves also.

Here is a passage from QM: "For all practical boundary conditions, the waves must be standing plane waves of all possible wavelengths and amplitudes"

What is the significant of saying "standing plane waves"? Author could have waves or plane waves but I think he is trying to convey by saying "standing plane waves".

Any help will be appreciated.
 
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  • #2
they're just plane waves that don't propagate but rather appear to stand still.
 
  • #3
An example of a standing plane wave whose planes are parallel to the xy-plane (i.e. perpendicular to the z-axis) is

[tex]\psi(x, y, z, t) = A \cos (kz) \exp (i \omega t)[/tex]
 

Related to What is the menaing of standing plane waves ?

1. What are standing plane waves?

Standing plane waves are a type of electromagnetic wave that appears to be standing still in space, as opposed to traveling in a particular direction. They are created when two waves with the same frequency and amplitude traveling in opposite directions interfere with each other.

2. What is the difference between standing plane waves and traveling plane waves?

The main difference is in the direction of propagation. Traveling plane waves move in a specific direction, while standing plane waves appear to be stationary. Additionally, traveling plane waves have a changing amplitude and phase as they move, while standing plane waves have a constant amplitude and phase.

3. How are standing plane waves used in science and technology?

Standing plane waves have a variety of applications in science and technology. They are commonly used in antenna design, where they can be used to create directional beams of radiation. They are also important in optics, as they can be used to create interference patterns and produce high-resolution images.

4. Can standing plane waves exist in all types of media?

Yes, standing plane waves can exist in any medium that can support electromagnetic waves. This includes both vacuum and various materials such as air, water, and solids. The properties of the medium, such as its refractive index, may affect the behavior of the standing plane waves.

5. What is the significance of standing plane waves in understanding wave behavior?

Studying standing plane waves can help us understand the fundamental principles of wave behavior, such as interference and superposition. They also have practical applications in various fields, making them an important area of study in science and technology.

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