We know that electrons have a dual nature just like EM waves (of course all the materials are said to have dual nature, noticeable or not). So looking at the wave nature of an electron and comparing this with photons, is it possible to make its kinetic energy equal to zero?
Copied form researchgate...
First of all, you can't compare photons with electrons. They are different types of particles (spin 1 vs spin1/2; force transmitter vs force emitter; see this question).
No, it's not possible to stop an electron. because of the simple fact, it has to obey the Heisenberg uncertainty relation with respect to place and momentum.
In the extreme case (theoretically) we can measure the electron's momentum with absolute certainty. Which means we know absolutely nothing about the whereabouts of the electron (Heisenberg). But how to find (or construct) such an electron? By an exact measurement? It would be a huge coincidence if the electron had indeed momentum zero. But this is all abstract and theoretical so, again, the answer is a big NO.
So looking at wave nature of electron
The wave nature of the electron is not a wave nature in space for the individual electron, but in the probability of measuring it at (x,y,z,t). When you measure an electron you get a footprint of its extent in space compatible with a point particle. This experiment shows individual electrons, and the accumulation of electrons shows the wave nature. The particle table has the electron as a point particle .
Let us suppose that in the decay of some particles an electron is measured, and the four momenta of the input and output particles are measured. One can use Lorenz transformations and go the the kinetic frame where the electron has zero momentum. In contrast to photons, massive particles have a system where they can be at rest.
Whether in the laboratory one can cool electrons enough so that they can be considered at rest with the techniques shown here needs a specialist's answer.
Here is an experiment that describes the cooling of electrons down to -228C. Even if one could have a gas of electrons at zero momentum, the repulsive forces between them would immediately set them moving.
Experiments that detect individual electrons rely on interactions of the electrons with some material. If they have zero momentum they would not be able to interact. That is why we have mathematical tools as the Lorenz transformations, and as they are validated for higher velocities, we accept their predictions for zero velocities.
Photons are pure kinetic energy.
Moreover, you could say the energy of a photon is purely kinetic energy.
Do photons have kinetic energy?
But photons are massless. Electrons on the other hand, do have rest mass. It is very confusing when somebody learns about rest mass and thinks electrons can actually be brought to rest. In reality they cannot be. No one has ever experimentally seen an actual electron at rest.
Due to the HUP, when you try to restrict the electron to a very small region of space, the electron's position will be known with high certainty, thus, the electron's momentum (kinetic energy) will have extreme uncertainty (will rise). And vica versa. If you try to restrict the momentum of the electron (cooling), the electron's position will be known with extreme uncertainty.
the uncertainty principle states that the more precisely the position of some particle is determined, the less precisely its momentum can be predicted from initial conditions, and vice versa.[2]
https://en.wikipedia.org/wiki/Uncertainty_principle
But I do understand where your question might come from. You can read phrases about electrons being standing (evanescent waves) as they exist around the nucleus.
The electrons do not orbit the nucleus in the manner of a planet orbiting the sun, but instead exist as standing waves.
en.wikipedia.org/wiki/Atomic_orbital
But this is very confusing because in reality electrons are quantum objects and cannot be brought to rest as per the HUP. This is QM.
No particle can be without kinetic energy in quantum mechanics. As the kinetic energy operator is $-\hbar^2 \partial_x^2 / 2m$, this would require a strictly position independent wave function. Of course an electron can easily have zero average momentum by capturing it in a Penning trap or on a point defect in silicon.
Of course an electron can easily have zero average momentum by capturing it in a Penning trap or on a point defect in silicon ...or, you know, just sticking it to a proton. Like in an atom.
– J...
Jan 11 '20 at 19:22