Matter waves as standing waves

The standing waves of matter waves associated with electrons are also confined within a specific range, making them similar to classical standing waves. However, the amplitude of matter waves can vary at different points within the confined range, which can lead to a dilemma in understanding their behavior. In summary, matter waves associated with electrons are regarded as standing waves because they are solutions to the time-independent Schrödinger equation, but they differ from classical standing waves in terms of their amplitude variation within the confined range.
  • #1
GAGS
55
0
Hi all,can anyone tell me the meaning of lines that i had read from a book:
"The electron is situated within a distance of 10 to the power -8 to 10 to the power -10 m. from the nucleus and is always confined only within this distace. The matter waves associated with electron is defined in terms of standing waves or stationary wave,which have varying amplitude at different points in the region and practically zero outside the range"
Now i have two questions
1.)Why matter waves associated with electron is regarded as standing wave?
2.)The definiton of standing wave says that amplitude is constant within a confined range,but here we are saying that amplitude is varying at different points within the range.
WHATS THAT DILEMMA?
please help me.
thanks
 
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  • #2
GAGS said:
1.)Why matter waves associated with electron is regarded as standing wave?
Because it is a solution to the time-independent Schrödinger equation, which is a wave equation.

GAGS said:
2.)The definiton of standing wave says that amplitude is constant within a confined range,but here we are saying that amplitude is varying at different points within the range.
A classical standing wave also has an amplitude that varies with position.
 

1. What are matter waves as standing waves?

Matter waves, also known as de Broglie waves, are a phenomenon in quantum mechanics in which particles such as electrons and protons exhibit wave-like behavior. These waves are referred to as "standing" because they do not propagate through space but instead oscillate in a fixed position.

2. How are matter waves as standing waves different from classical waves?

Matter waves are fundamentally different from classical waves in that they are not caused by a disturbance in a medium, but rather are an intrinsic property of particles. Unlike classical waves, matter waves do not require a medium to propagate and can exist in a vacuum.

3. What is the significance of matter waves as standing waves?

The existence of matter waves as standing waves was a major discovery in the development of quantum mechanics. It provided further evidence for the wave-particle duality of matter and helped to explain phenomena such as the diffraction and interference of particles.

4. How are the properties of matter waves as standing waves determined?

The properties of matter waves, such as wavelength and frequency, are determined by the momentum and energy of the particle. This is described by the de Broglie equation, which relates the wavelength of a particle to its momentum. The higher the momentum, the shorter the wavelength and the higher the frequency of the matter wave.

5. Can matter waves as standing waves be observed experimentally?

Yes, matter waves as standing waves have been observed experimentally through various techniques such as electron diffraction and matter wave interferometry. These experiments have provided strong evidence for the wave-like nature of particles and have further advanced our understanding of quantum mechanics.

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