Author: haroonkhan
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Uncertainty in a Macroscopic World
All of this weird uncertainty doesn’t seem to bother us in everyday life. Why not? Once again, it’s all a matter of scale. Heisenberg showed that the product of the uncertainties of conjugate pairs of observables can be about as small as Planck’s constant, but no smaller. But since Planck’s constant itself is extremely small…
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Conjugate Pairs
It turns out that Heisenberg’s uncertainty principle applies to pairs of observable things, and only to certain pairs. The technical name for these is conjugate pairs. We don’t need to go into all the conjugate pairs of observables or why they are conjugate, or even what in the world “conjugate” really means, but it will be…
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The Heisenberg Uncertainty Principle
The position of a moving particle is not the only thing that is a little fuzzy in quantum physics. It turns out that there is a very interesting interaction between the position and the momentum of a particle. The relationship between the uncertainties in these two quantities is something that does not appear at all…
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The Role of Probability
It is not possible to predict exactly where any individual photon (or electron) will land after traversing the double slits. But since we observe a striped pattern, we can say that the probability of seeing a photon must be higher at certain positions than at others. The probability is high where the amplitude of the…
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Quantum Waves
We made a big deal about the use of mathematical models to describe physical phenomenon. Now we’ll take a crack at seeing not only how this can be done, but why it turns out to be so useful. And, given the emphasis we’ve been placing on matter waves, it’s probably no surprise that our starting…
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Introduction
We will make a quantum jump of our own. Until now, we’ve been able to present a logical progression of quantum ideas that tracked, for the most part, with the historical development of quantum physics. By the early 1920s however, its development diverged into several different, though intimately linked, paths. We will visit each in…
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Double-Slit Redux
As you have probably guessed, the best measurement to exemplify wave-particle duality in matter is the good old double-slit experiment. If a beam of electrons is directed through a pair of narrow slits (where the spacing between the slits is comparable to the de Broglie wavelength of the electrons), peculiar things begin to happen. When…
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A Second Look at Wave-Particle Duality
So somewhere along the line, as you go smaller and smaller from planets to potatoes to protons, things that normally behave like classical massive particles start to display wavy characteristics. It is not a sharp transition, and there is no exact size where we can say larger things are just particles and smaller things are…
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Protons, Potatoes, and Pluto
De Broglie’s relation is general and applies to any particle, large or small. Every moving mass has the potential to display interference and other wave properties. So why didn’t we notice this before 1927? And why don’t we see it all around us now that we know it’s there? Once again, it’s all a question…
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The Davisson-Germer Experiment
As we’ve known since the days of Newton, a particle’s momentum is directly proportional to its mass. For a massive particle with large momentum, the size of Planck’s constant makes the de Broglie wavelength very small, even when compared to the wavelengths of light. This made it quite challenging to observe any wavelike behavior of…