What is De Broglie's Fictitious Wave?

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SUMMARY

De Broglie's concept of fictitious waves is central to understanding the wave-particle duality in quantum mechanics. He presents two equations, v' = v SQRT(1-Beta^2) and v' = v / [SQRT(1-Beta^2)], which illustrate the discrepancies in energy transformation from different frames of reference. The discussion highlights the confusion surrounding the second fictitious wave that De Broglie proposes to resolve these contradictions. Ultimately, the consensus suggests that studying quantum mechanics through established texts, such as Ballentine's, may provide clearer insights.

PREREQUISITES
  • Understanding of wave-particle duality in quantum mechanics
  • Familiarity with Lorentz transformations in special relativity
  • Basic knowledge of De Broglie's original theories and equations
  • Experience with quantum mechanics textbooks, particularly Ballentine's
NEXT STEPS
  • Study De Broglie's original paper on wave-particle duality
  • Examine Lorentz transformations and their implications in quantum mechanics
  • Read Ballentine's "Quantum Mechanics" for a comprehensive understanding
  • Research the concept of fictitious waves and their role in quantum theory
USEFUL FOR

Students of quantum mechanics, physicists exploring wave-particle duality, and anyone seeking to clarify the complexities of De Broglie's theories.

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I read through DeBroglie's original paper - and also a modern explanation on the same (attached).
The first contradiction that DeBroglie arrives at is simple enough - he considers the 'wave-particle' as observed from a stationary frame - and from a moving frame. The 'inner frequency' of the wave-particle is
v' = v SQRT (1-Beta^2) Equation (1)
Now, he looks at the Energy transformation - and arrives at - v' = v / [SQRT (1-Beta^2)]. equation (2)

(1) and (2) are different - that is plain to see. To explain this difference, de-Broglie assumes ANOTHER fictitious wave associated with the particle. This is the part I am having trouble with - can anyone shed light on this second wave - and how it resolves the dilemma?

Page 2 in the attached article discusses this fully.
 

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What can one say - De Broglie is a crock.

Forget about it - study QM from a book like Ballentine.

Thanks
Bill
 

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