Calculating total energy of particles

How do you find the total energy of a proton whose kinetic energy is, say, 8.5 GeV?

How is the Heisenburg Uncertainty Principle taken into account?

 

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You mention the UP so are you coming at this from a QM point of view or a relativistic one?

For a relativistic point of view a proton has a rest mass of about 1GeV so a KE of 8.5GeV is going to make it quite relativistic and you have to use the usual equation \(E^{2} = (mc^{2})^{2} + |\mathbf{p}c|^{2}\).

If you want a more QM based point of view you get into things like expectation values for the Hamiltonian. Then its a question of what you're viewing the proton in terms of. Is it a bound state of quarks held together by gluons (which makes it a mind-blowingly complicated non-perturbative QCD problem) or just a particle with a particular wave function?

 

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Could it be found using the energy-time uncertainty?

 

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And to answer your question, let's go with a particle as a wave function.