I Freqeuncy of Matter Waves Approaches Infinity as Velocity Approaches c

hisgutsaysmaybe
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If phase velocity = fλ, and as group velocity -> c, λ -> 0 but phase velocity -> c, then does this mean that f -> infinity as group velocity -> c?
I have heard that the phase velocity of matter waves can be represented as c^2/v. But if the wavelength of these matter waves goes to zero as momentum approaches infinity and v approaches c, then does this mean that the frequency of the matter waves approaches infinity, to give the matter wave a finite and nonzero speed?
In a way this might make sense, because E = ymc^2, so hf = ymc^2. However, the time of an event dilates for an observer which is moving with respect to the event, also by a factor of gamma. I had believed that these two phenomena might combine to appear to give the matter wave a constant frequency, regardless of the velocity of the observer.
 
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hisgutsaysmaybe said:
I have heard
Where? Please give a reference.
 
From De Broglie's 1924 paper, page 10 (445 of the journal):
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Taken from this PDF version: https://www.pwein.at/physics/Lectures/Famous-Papers/Phil-Mag-47-446-1924.pdf

I learned in school that the phase velocity was c^2/v, and I have taken it as fact without trying to understand why yet.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!
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