Is Total Energy Always Double the Kinetic Energy in Quantum Mechanics?

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Total energy in quantum mechanics is not always double the kinetic energy, particularly when distinguishing between ordinary particles and photons. The equations E = hf and λ = h/p apply differently; E = hf is specific to photons, while kinetic energy for ordinary particles is given by p²/2m. The confusion arises from applying photon equations to particles with mass, as photons exhibit unique properties. The relationship p = h/λ holds for both, but the energy equations differ fundamentally. Thus, the assumption that total energy equals double kinetic energy is incorrect for non-photon particles.
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Homework Statement



Ok so (1) E = hf and (2) lambda = h/p


Homework Equations





The Attempt at a Solution



For a particle mass m, speed v, momentum p

Surely if p^2 / 2m = Ek (kinetic energy)

then we can write from (2) Ek = h^2/ 2m lambda^2

But from (1) we can write E = hv/lambda => E = h(p/m)/lambda => E = h^2 / m lambda^2

This seems to imply that for such a particle total energy is always double KE. What's gone wrong?
 
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p^2 / 2m = Ek applies to ordinary particles, not photons.
Photons are WEIRD. The fact that p = h/λ applies to both is incredible and I think de Broglie thought of it while drinking beer.
 
Yes but I am talking about an ordinary particle here..
Does E=hf not work for ordinary particles?
 
E = hf applies to photons only.
 
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