De broglie vs classical wavelength

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SUMMARY

The discussion centers on the relationship between de Broglie wavelength and classical wavelength, particularly in the context of photons and electrons. The de Broglie wavelength, defined as λ = h/p, is not interchangeable with classical wavelength in all scenarios, especially when considering particles with mass like electrons. For photons, the equations E = hf and E = hc/λ apply directly, while for electrons, the momentum p must account for both kinetic and rest mass energy, complicating the relationship. The discussion highlights that the wave relationship is valid primarily for massless particles, with distinctions made between phase and group velocities.

PREREQUISITES
  • Understanding of quantum mechanics concepts, specifically de Broglie wavelength.
  • Familiarity with the equations E = hf and E = hc/λ.
  • Knowledge of momentum in the context of relativistic particles.
  • Basic grasp of wave-particle duality and its implications for massless vs. massive particles.
NEXT STEPS
  • Study the derivation and implications of the de Broglie wavelength for massive particles.
  • Learn about the differences between phase velocity and group velocity in wave mechanics.
  • Explore the implications of relativistic momentum on particle energy and wavelength.
  • Investigate the role of rest mass in quantum mechanics and its effect on wave equations.
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Students and professionals in physics, particularly those focusing on quantum mechanics, wave-particle duality, and the behavior of electrons in various energy states.

xiankai
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since it is defined (from what i can tell) as h/p,

is it interchangeable with the classical wavelength in equations involving waves in general? or is it a special separate case for matter?

that is,

for photons we have the following equation:
E = hf
E = hc/λ

can the same equation be used to find the wavelength/energy of electrons?
 
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The de Broglie wavelength is now kinda viewed as the characteristic "size" of a quantum particle. It's not really a super-relevant physical quantity anymore, nor can you just put it into classical wave equations to get anything physical.
 
xiankai said:
since it is defined (from what i can tell) as h/p,

is it interchangeable with the classical wavelength in equations involving waves in general? or is it a special separate case for matter?

that is,

for photons we have the following equation:
E = hf
E = hc/λ

can the same equation be used to find the wavelength/energy of electrons?
For a photon E=pc, so the dB wavelength for a given energy is simple.
For an electron p=\sqrt[{E^2/c^2-m^2}, so the dB wave length in terms of energy is more complicated,.
 
Meir Achuz said:
For a photon E=pc, so the dB wavelength for a given energy is simple.
For an electron p=\sqrt[{E^2/c^2-m^2}, so the dB wave length in terms of energy is more complicated,.

we must include the rest mass of the electron?
 
Yes. And to get the frequency of the wave via E = hf, you must use the total energy (kinetic energy plus rest energy).
 
According to de broglie relation lambda=h/mv ...which implies that velocity is inversely proportional to wavelength. But According to the reletion

V=n lambda ... velocity is directly proportional to wavelength... How That diffenence is Causesd ? Am i going wrong Somowhere ?
 
Note that the wave relationship only holds for massless particles.
 
The V in V=\nu\lambda is the phase velocity of the traveling wave packet.
This V also = E/p=h\nu/p, which is consistent.
The phase velocity is >c, but the group velocity v_G=p/E is less than c.
 

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