If we want to measure where the particle is we have to put some energy in, but then of course the system is no longer at absolute zero and the momentum is now non-zero. The uncertainty principle implies that it is in general not possible to predict the value of a quantity with arbitrary certainty, even if all initial conditions. In that case, at absolute zero the momentum is zero but then we have no knowledge about where the particle is (i.e. The situation is different for a free particle. This is most obvious for light atoms like Helium where the zero point energy is enough to keep the system liquid, so even at absolute zero Helium will not solidify unless it's put under pressure. There will be a small vibration corresponding to the zero point energy. This means that at absolute zero the atoms in a crystal will not be stationary. The uncertainty principle in its standard form describes how precisely we may measure the position and momentum of a particle at the same time if we increase the precision in measuring one quantity, we are forced to lose precision in measuring the other. crystals, at low temperatures the atoms/molecules behave as harmonic oscillators, and the energy of a harmonic oscillator cannot be reduced to zero: there is always some minimum energy called the zero point energy. Furthermore, it shows that there is a definite relationship to how well each can be known relative to the other. The Heisenberg uncertainty principle is a law in quantum mechanics that addresses limitations in the accuracy of measuring two variables. Motion does not cease at absolute zero if the system you are looking at has a zero point energy. The Heisenberg Uncertainty Principle Equation is the mathematical expression of the fact that the position and velocity of a particle cannot be known simultaneously.
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