Planck's law and doppler effect

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SUMMARY

The discussion centers on deriving Planck's Law, expressed as E=h*u, from the Doppler effect equation u'=u*√((1-β)/(1+β)). The participant attempts to connect the Lorentz transformation and the energy-momentum relationship, ultimately questioning the sufficiency of the Doppler effect alone to derive the energy of a photon. Key equations referenced include the Lorentz transformation and the energy-momentum relation E'=y(E-B*Px*c). The conclusion emphasizes the need for additional information beyond the Doppler effect to fully understand the derivation.

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  • Understanding of Planck's Law and its implications in quantum mechanics.
  • Familiarity with the Doppler effect and its mathematical representation.
  • Knowledge of Lorentz transformations in the context of special relativity.
  • Basic concepts of energy-momentum relationships in physics.
NEXT STEPS
  • Study the derivation of Planck's Law from first principles in quantum mechanics.
  • Explore the implications of the Doppler effect in both classical and relativistic contexts.
  • Investigate the relationship between energy and frequency in quantum physics.
  • Review advanced topics in special relativity, focusing on energy-momentum conservation.
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Students of physics, particularly those studying quantum mechanics and special relativity, as well as educators seeking to clarify the relationship between Planck's Law and the Doppler effect.

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Hello, We proved something during the course but I totally forgot how to do it..

Homework Statement


Prove that Planck's Law E=h*u is deduced from the equation of Doppler effect u'=u*√((1-β)/(1+β))

Homework Equations


Lorentz transformation

The Attempt at a Solution


If we take a beam of light of frequency u and an observer with speed Bc
I don't know if it's correct..
u'=u√((1-β)/(1+β))
E'=y(E-B*Px*c)
And px*c=E so
E'=y(E-BE)
=yE(1-B)
=E√((1-β))/(√((1-β)/(1+β)))
=E√((1-β))/√(1+β)
E'=E*u'/u
E'*u=E*u'
E'/u'=E/u
E/u=cste=h ?
 
Last edited:
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I don't think that the energy of a photon can be derived solely from a consideration of the Doppler effect (relativistic or not). More information is needed.
 

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