What is the wavelength of an object at rest according to de Broglie's equation?

In summary, the wavelength of an object at rest (v=0) cannot be precisely defined due to the uncertainty principle. The best approximation would be a wave packet with a range of momentums centered around zero, resulting in a standing wave with maximum amplitude at the most likely location of the particle. This is necessary in order to satisfy the uncertainty principle.
  • #1
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if de Broglie's equation: wavelength = h/(mv) works allways, then what is the wavelength of an object at rest (v=0) is it undefined or infinity or something?
 
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  • #2
Because of the uncertainty principle, you can't have a wave function for a particle that is definitely exactly at rest, just as it can't have any other definite exact value of momentum (and velocity).

The best you can do for a "stationary" particle is a wave packet whose momentum has an expectation value of zero, and includes waves with both positive and negative values of momentum, in a range that is centered on zero. I suspect that such a wave packet would be a standing wave with maximum amplitude at the most likely location of the particle, and decreasing to zero in either direction so the width and the momentum range satisfy the uncertainty principle.
 
  • #3


According to de Broglie's equation, the wavelength of an object is inversely proportional to its momentum. Therefore, if an object is at rest and has no momentum (v=0), its wavelength would be undefined or infinite. This is because the equation would involve dividing by zero, which is mathematically undefined. However, in practical terms, the wavelength of an object at rest is not relevant as it would not exhibit any wave-like properties. It is only when an object is in motion that its wavelength becomes significant.
 

FAQ: What is the wavelength of an object at rest according to de Broglie's equation?

What is the wavelength of matter at rest?

The wavelength of matter at rest is typically referred to as the de Broglie wavelength, named after physicist Louis de Broglie. It is a measure of the wavelength associated with a particle's wave-like behavior.

How is the wavelength of matter at rest calculated?

The de Broglie wavelength can be calculated using the formula λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of the particle, and v is the velocity of the particle.

What is the significance of the wavelength of matter at rest?

The de Broglie wavelength is significant because it shows that even particles with mass, such as electrons and protons, exhibit wave-like properties. This helped to bridge the gap between classical mechanics and quantum mechanics.

Does the wavelength of matter at rest change?

Yes, the de Broglie wavelength of a particle can change depending on its velocity. As the velocity of a particle increases, its wavelength decreases.

How is the wavelength of matter at rest related to Heisenberg's uncertainty principle?

The de Broglie wavelength is related to Heisenberg's uncertainty principle, which states that it is impossible to know both the precise position and momentum of a particle at the same time. The de Broglie wavelength represents the uncertainty in the momentum of a particle at a given moment.

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