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phyky

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The question as stated in title, why?

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- Thread starter phyky
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In summary, the deBroglie wavelength is a concept introduced as λ = h/p, where h is Planck's constant and p is momentum. It is used to describe the wavelength of a particle, particularly in relation to relativity and non-relativity in physics. It can also be approximated using the rest mass (m) and velocity (v) of the particle. The velocity of the deBroglie wavelength is related to both the phase velocity (vp) and group velocity (vg), with the equation λ = h/mvg. There is some confusion about whether the deBroglie wavelength refers to the wavelength of the electron or the phase wavelength that guides the electron, as well as the role of phase velocity in a

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phyky

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The question as stated in title, why?

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tom.stoer

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But b/c the rel. expression for p can be approximated with the non-rel. expression for v << c we also have a non-rel. approximation for the wavelength, namely λ = h / mv (m: rest mass).

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phyky

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phyky

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The De Broglie wavelength is a concept in quantum mechanics that describes the wave-like nature of particles. It is named after physicist Louis de Broglie, who proposed that all particles, such as electrons and protons, have both particle-like and wave-like properties. The De Broglie wavelength is the wavelength associated with a particle's momentum, and it is given by the equation λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle.

The De Broglie wavelength can be derived from Einstein's theory of relativity, specifically the equation E = mc². This equation relates a particle's energy (E) to its mass (m) and the speed of light (c). By rearranging this equation, we can find that p = E/c, where p is the momentum of the particle. Substituting this into the De Broglie wavelength equation, we get λ = h/(E/c). Since the energy of a particle is related to its mass by E = mc², we can rewrite the equation as λ = h/(mc), which is the same as the De Broglie equation.

Even though the De Broglie wavelength is derived from relativity, it can still be used in non-relativistic situations. In these cases, the mass of the particle is much larger than its energy, so the term mc in the equation is small and can be ignored. This simplifies the equation to just λ = h/p, which is the same equation used in non-relativistic situations.

The De Broglie wavelength is significant in quantum mechanics because it helps to explain the wave-particle duality of particles. It suggests that particles, which were previously thought to be only particles, also have wave-like properties. This has been confirmed by numerous experiments, such as the double-slit experiment, where particles behave like waves and exhibit interference patterns. The De Broglie wavelength also plays a crucial role in the uncertainty principle, which states that the position and momentum of a particle cannot be known simultaneously.

Yes, the De Broglie wavelength has been observed in many real-life situations. One example is the electron microscope, where electrons are accelerated to high speeds and their wave-like nature is observed. Another example is in particle accelerators, where particles are accelerated to near-light speeds and their De Broglie wavelengths become significant. The De Broglie wavelength is also used in various technologies, such as electron microscopy and scanning tunneling microscopy, to study the wave-like nature of particles and their interactions with matter.

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