Heisenberg Uncertainty Principle
The Heisenberg Uncertainty Principle States That the Position and the Momentum of a Particle Cannot Be Specified Simultaneously with Unlimited Precision.
We now know that we must consider light and matter as having the characteristics of both waves and particles. Let’s consider a measurement of the position of an electron. If we wish to locate the electron within a distance ∆x, then we must use a measuring device that has a spatial resolution less than ∆x. One way to achieve this resolution is to use light with a wavelength on the order of λ ≈ ∆x. For the electron to be “seen”, a photon must interact or collide in some way with the electron, for otherwise the photon will just pass right by and the electron will appear transparent. The photon has a momentum p = h/ λ, and during the collision, some of this momentum will be transferred to the electron. The very act of locating the electron leads to a change in its momentum.
If we wish to locate the electron more accurately, we must use light with a smaller wavelength. Consequently, the photons in the light beam will have greater momentum because of the relation p = h/ λ. Because some of the photon’s momentum must be transferred to the electron in the process of locating it, the momentum change of the electron becomes greater. A careful analysis of this process was carried out in the mid-1920s by the German physicist Werner Heisenberg, who showed that it is not possible to determine exactly how much momentum is transferred to the electron. This difficulty means that if we wish to locate an electron to within a region ∆x, there will be an uncertainty in the momentum of the electron. Heisenberg was able to show that if ∆p is the uncertainty in the momentum of the electron, then
∆x ∆p ≥ h/4π ……(1)
Equation 1 is called Heisenberg’s Uncertainty Principle and is a fundamental principle of nature. The Uncertainty Principle states that if we wish to locate any particle to within a distance ∆x, then we automatically introduce an uncertainty in the momentum of the particle and that the uncertainty is given by Equation 1. Note that this uncertainty does not stem from poor measurement or experimental technique but is a fundamental property of the act of measurement itself. The following two examples demonstrate the numerical consequences of the Uncertainty Principle.
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