This is the second part of the explanation of Heisenberg's Uncertainty principle, with this one being the proper explanation. This basic concept is that we cannot know both the particle's momentum and its location very precisely at the same time. We can either know the momentum very precisely and the location very vaguely or thee other way round. In this statement, Heisenberg is in no way commenting on the way we conduct the experiments or the instruments we use to collect the data. He is talking about the wavefunction of the particle itself, which we discussed in the last post on the De Broglie equation.
As the particle we address gets smaller, it is less and less appropriate to call it a hard sphere and more as a wave. And so, when this happens, we use the quantum mechanical wavefunction in order to determine the probability of the particle being in certain locations. For example, A perfect sinewave for an electron's wavefunction spreads out the probability throughout the space so that the probability of it being at a given location is the same everywhere and we cannot know even the rough location o the electron. However, due to the equation " p=h/wavelength", if the wavelength is perfectly known (due to it being a sine wave), then we should also know its exact momentum, giving us the velocity of the particle because momentum is the product of a particle's mass and velocity (p=mv). However, adding together several waves of different wavelength will produce an interference pattern which will add up the probabilities of where the particle could be so that the probability of it being in some places is higher while it is lower for others. This allows us to locate the particle more precisely. However, doing this, will spread out the wavelength of the wavefunction and in turn make the momentum value more imprecise.
As the particle we address gets smaller, it is less and less appropriate to call it a hard sphere and more as a wave. And so, when this happens, we use the quantum mechanical wavefunction in order to determine the probability of the particle being in certain locations. For example, A perfect sinewave for an electron's wavefunction spreads out the probability throughout the space so that the probability of it being at a given location is the same everywhere and we cannot know even the rough location o the electron. However, due to the equation " p=h/wavelength", if the wavelength is perfectly known (due to it being a sine wave), then we should also know its exact momentum, giving us the velocity of the particle because momentum is the product of a particle's mass and velocity (p=mv). However, adding together several waves of different wavelength will produce an interference pattern which will add up the probabilities of where the particle could be so that the probability of it being in some places is higher while it is lower for others. This allows us to locate the particle more precisely. However, doing this, will spread out the wavelength of the wavefunction and in turn make the momentum value more imprecise.
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