What would be likely to completely stop a subatomic particle assuming it was possible? Suppose that completely stopping a subatomic particle, such as an electron, could happen under certain conditions. What would be likely ways to get an electron to be perfectly still, or even just stop rotating the nucleus and collapse into it by electromagnetic forces? What would likely be required, below absolute-zero temperatures? Negative energy? Or could a 0 energy rest state not exist in any form, of any possible universe imaginable?
Let's say there was a magnetic field of a certain shape that we could postulate that is so intensely strong that if we put an electron in the center of it, it could not move at all in any direction. Would the energy requirement of the field be infinite? What would be the particle's recourse under this condition?
Further, suppose it were possible and one could trap an electron and stop all motion completely. What would this do to Heisenberg's Uncertainty Principle and/or Quantum Mechanics, because its position and momentum (0) would both be known? If it can be done, is Quantum Mechanics no longer an accurate model of reality under these conditions? Could we say QM is an accurate model under most conditions, except  where it is possible to measure both position and momentum of a particle with zero uncertainty?
Clarification:
Please assume, confined in a thought experiment, that it IS possible to stop a particle so that is has 0 fixed energy. This may mean Quantum Mechanics is false, and it may also mean that under certain conditions the uncertainty commutation is 0. ASSUMING that it could physically be done, what would be likely to do it, and what would be the implications on the rest of physics?
Bonus Points
Now here's the step I'm really after - can anyone tell me why a model in which particles can be stopped is so obviously not the reality we live in? Consider the 'corrected' model is QM everywhere else (so all it's predictions hold in the 'normal' regions of the universe), but particles can be COMPLETELY stopped {{inside black holes, between supermagnetic fields, or insert other extremely difficult/rare conditions here}}. How do we know it's the case that because the uncertainty principle has lived up to testing on earth-accessable conditions, that it holds up under ALL conditions, everywhere, for all times?
 A: This is just a misunderstanding--- "no motion" in quantum mechanics is a different concept than "no motion" in classical mechanics. At zero temperature, nothing stops. Spherical uncharged black holes don't stop particles at the singularity, they absorb particles and time just ends at the singularity for the infalling matter. The wavefunctions are not made to stop.
You can stop an electron by putting it in the ground state of Hydrogen. This is what it means to be stopped in quantum mechanics.
The reason one can be sure that the uncertainty principle applies to more than what we have seen is that it is impossible to make part of the world classical and part quantum mechanical, as understood by Bohr and Rosenfeld in the early days of quantum mechanics. The fact that the electron has an uncertainty principle means that there would be a contradiction if something else did not, because this would allow you to violate the uncertainty principle for electrons by interacting them with this new thing.
If the world is classical underneath, the classical variables will have very little relation to the position and momentum of classical point particles. This question is annoying, and it does not deserve any more attention than what it has gotten.
A: Your question is interesting, and gets specifically to the kinds of questions that quantum mechanics was intended to answer in the first place.  It helps to understand the motivation behind the original Bohr model of the atom, and how that led to QM in the first place. 
The problem Bohr was trying to address can be paraphrased as, "If an electron orbits a nucleus like a planet, why doesn't it gradually lose energy and spiral into the nucleus?"  The answer came when Bohr realized that the orbital momentum was quantized, effectively meaning that since the electron had mass then by the relationship $p=mv$, the velocity was also quantized (note: this simple expression is more complicated when relativity is included, but the discussion can continue without including it).  These quantized values of momentum/velocity are what one would call eigenvalues, or observables in quantum mechanics. Since the electron can only change orbits by given off specific quantities of energy instead of giving off energy continuously, it remained in a stable orbit relative to the nucleus, thus preventing it from spiraling in. 
What is important to understand is the idea of the potential well.  In the Bohr model, the electrons closest to the nucleus have higher velocity than the electrons further away.  In other words, they have greater kinetic energy ($K.E. = \frac{1}{2} mass \times velocity^2$), but it had less potential energy since it was closer to the nucleus (obeying the relationship $P.E. = mass \times distance \times gravity$).  However, the total energy ($K.E. + P.E.$) associated with orbits closer to the nucleus is less than those further away.  So in order for the electron to move closer to the nucleus, energy must be given up.  This is accomplished by the emission of a photon.  Alternatively, if one wants to cause an electron to move into a more distant orbit, then one must add energy through use of a photon.
It is in contemplating how to determine the orbit of the electron that the uncertainty principle first became apparent.  The only probe that we have available to determine the position of an electron in its orbit is a photon, and the photon must be of sufficient energy in order for it to be small enough to give a meaningful result, however if we use a photon small enough (in terms of wavelength), it will have enough energy to shift the electron into a different orbit, and then we would have to start the process all over again.  
A free electron has sufficient energy to escape the nucleus.  In other words, it has acquired sufficient energy to fill its potential energy deficit.  If there were only one nucleus in the universe, the potential deficit would only be eliminated when the electron was at infinite distance from the nucleus.  In that situation, the implication is that the electron would also have zero velocity.  This situation is obviously unrealistic, first there are more than one nuclei in the universe, and second, to verify that a particle has zero velocity at infinite distance is clearly an impossible task.
If we move past the Bohr model and into more modern quantum mechanics, the question then is whether there are eigenstates that have eigenvalues for momentum of a particle that are equal to zero?  It is important to review some basic facts about matrix operations and linear algebra

If 0 is an eigenvalue of a matrix A, then the equation A x = λ x = 0 x = 0 must have nonzero solutions, which are the eigenvectors associated with λ = 0. But if A is square and A x = 0 has nonzero solutions, then A must be singular, that is, det A must be 0. This observation establishes the following fact: Zero is an eigenvalue of a matrix if and only if the matrix is singular. 

This means that the matrix in question is not of full rank.  In QFT this has a very specific interpretation.  The annihilation operator has the power to destroy the vacuum state and map it to zero.  This situation is understood to be associated with the free field vacuum state with no particles.  This state is necessary because it allows us to find vacuum state solutions for the associated quantum mechanical system.  
By means of analogy, we can see that the solution to ground state problem is the solution to the homogeneous part of a differential equation.  
The Schrodinger equation is a linear, homogeneous equation which governs evolution of the wave function of a particle.  The solutions of the Schrodinger equation can be used to understand particle motion.  The exact position and momentum of a particle can only be known if h (planck's constant) approaches zero, however, in quantum mechanics, planck's constant is fundamental to the theory, so this cannot occur in the single particle case.  Because of this, momentum and position uncertainty establish an inverse relation to each other, and if the uncertainty of momentum is zero, then the uncertainty in position is infinite.  
For these reason's it is not possible to talk about a particle "stopping" or being "stopped" in any meaningful or non-contrived sense. 
A: There exists a huge number of experimental evidence that in the subatomic world nature is using quantum mechanics. In quantum mechanics bound states always have the first energy level above 0 energy. Your magnetic field thought experiment creates a bound stated in the collective potential.
Free states have to obey the HUP and therefore cannot have 0 fixed energy. 
Your question is another form of trying to impose the classical thinking of macroscopic physics to the microcosm; it cannot be done because  it has not been done after numerous experiments.
Edit 
An analogy: Take the ocean and a tiny volume  dV on the surface of it. This volume bobs up and down depending on the wave activity, and there is always some wave activity in the ocean. Does it make sense  to ask "under what circumstances will this dV be at rest with respect to the earth?"  "Could one use special waves to keep this specific dV motionless?".
The subatomic particles are probability waves and at that level one has as little control as in the ocean picture as far as localization goes, because any fields one can use at the subatomic level are also probability waves. Now we happen to have a solid theory with QM which can predict for us mathematically that there will always be some energy associated with a subatomic particle that will not allow it to be at rest, so we do not need to handwave, as with the ocean where we can only use statistical arguments.
Edit2
Ehryk : A thought experiment in physics has to start with the known physics data and theories  and extend it to uncharted territory. What everybody is telling you is that the known physics theories that have fitted perfectly all known experimental data, tell us that even in a thought experiment using known theories there cannot be a "stopped" particle in the microcosm.
Of course there can be science fiction physics, i.e. where one assumes new laws of physics. Then the burden is on the one who suggests these new laws to suggest experiments that will validate them. To imagine situations that have not been observed ever and are not in the realm of accepted theoretical calculations means science fiction.
Now if there were an experiment with solid data that demonstrated a "stopped particle" or "stopped particles" then every physicist would look up and scramble to try and understand it.
This is a physics board, and ultimately physics is about experimental data fitted by theories, not random models of how natural laws could be.
A: For a long time people have been interested in ultra low temperatures (as far as I know the current reccord is 0.1 nanokelvin). In this range of temperature, QM is all but desappearing. On the contrary, we observe long range QM effects, all observations tends to show that QM waves strech up and overlap. The most popular example is Bose Einstein condensates but it has also been shown that ultra-cold gas can chemically react at distances up to 100 times greater than they can at room temperature (Science 12 February 2010: Vol. 327 no. 5967 pp. 853-857 )
A: you have provided your own answer: as long as the uncertainty conmutation relations hold (and it does hold, have no doubt about it), there is no going to be such a thing as standing perfectly still for particles. 
But wait, there is the quantum zeno effect, which does a similar thing, but not quite the same as you ask; it keeps the quantum state from evolving.
See a related question: Quantum Zeno effect and unstable particles
A: It is quite easy to make electron to stop (that is make it having zero impulse and kinetic energy). But once it has zero impulse, it is smoothed over a volume. You can see it as having big dimensions rather than being point-like.
A: I think the prediction for motion stoppage at absolute zero applies to the atoms and molecules themselves, and not the internals (subatomic) of the atoms.  In other words, the atoms or molecules should have zero translational, rotational, and vibrational motion (kinetic energy) at absolute zero.
However with subatomic particles, in this topic the electron, cannot slow down with temperature.  In a given orbital around the nucleus, the electrons travel at a constant speed, a tiny bit less than the speed of light, regardless of temperature. 
Temperature is defined as a measure of the average kinetic energy of the atoms or molecules within a defined volume.  This macroscopic classical measurement is independent of the subatomic quantum realm where superposition, probability waves, electron shell orbitals, electron spin, and Heisenberg uncertainty principle applies.
Higher temperatures cause photons to be absorbed by the electrons, which in turn, cause the electrons to go to higher quantum orbitals around the nucleus, and given enough energy, the electron can escape the Coulomb attraction of the nucleus.  However, once the electron is settled in its quantum orbital level determined by the Pauli Exclusion principle, its speed is constant and cannot slow down.
According to the Bohr model of the atom, the electron stays in the orbital around the nucleus because of the equilibrium between the centripetal force of the electron away from the nucleus and the Coulomb force (electrostatic attraction) toward the nucleus.
centripetal force of orbiting electron outward = Coulomb force attraction inward.
If the electron slowed down with temperature then it would fall into the nucleus since the Coulomb Force we know is constant and independent of temperature.  Since electrical charge does not vary with temperature, neither should the speed of the electron.
So to answer your question, if you can come up with data or reason that shows that the Coulomb force, or for that matter, any of the other fundamental forces; magnetic, strong and weak nuclear force, or gravitational/inertial forces; vary with temperature, then we can theorize on a model that can explain varying the speed of or "stopping" electons or other subatomic particles.
