Can the energy of a particle ensemble in QFT be bounded over time?

[LeandroMdO]

Thanks @LeandroMdO - so you would say that the continuous momentum function is simply an approximation? But certainly provides accurate predictions over any range we can measure...

It's not the continuity that is an approximation, but the choice of a wave packet with a Gaussian form. In reality it doesn't have to be Gaussian. We use Gaussians for convenience of study and because the central limit theorem ensures it's a good approximation for many relevant situations.

 

[asimov42]

Sorry @LeandroMdO - I should have said continuous and non-zero over the whole real line? A continuous function could have a value of zero, of course.

 

[PeterDonis]

You just construct a single-particle state with a square-integrable wave function in momentum space

This is a free particle wave packet, so it would not describe, for example, an electron bound in an atom. The OP is talking about making a measurement of momentum on an electron in such a bound state. Scattering theory, which is basically what the wave packet you wrote down applies to, cannot be used in such a case.