According to de Broglie's wave-particle duality, the relation between electron's wavelength and momentum is λ=h/mv.
The proof of this is given in my textbook as follows:
De Broglie first used Einstein's famous equation relating matter and energy, E=mc2,
where E= energy, m= mass, c= speed of light.Using Planck's theory which states every quantum of a wave has a discrete amount of energy given by Planck's equation, E=hν,
where E= energy, h= Plank's constant (6.62607×10−34Js), ν= frequency.Since de Broglie believes particles and wave have the same traits, the two energies would be the same: mc2=hν.
Because real particles do not travel at the speed of light, de Broglie substituted v, velocity, for c, the speed of light: mv2=hν.
I want a direct proof without substituting v for c. Is it possible to prove directly λ=h/mv without substituting v for c in the equation λ=h/mc?
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