Category: The Quantum Wave Function

Once you do get to the scale of atoms and smaller, things certainly do get counterintuitive and distinctly nonclassical. We have seen many examples now. Particle position gets blurry. Particles seem to be governed by invisible wave functions. Particles interfere with themselves after passing through or around obstacles. We can’t tell which slit the photon… Continue reading The End of Determinism

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… Continue reading Uncertainty in a Macroscopic World

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… Continue reading Conjugate Pairs

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… Continue reading The Heisenberg Uncertainty Principle

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… Continue reading The Role of Probability

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… Continue reading Quantum Waves

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… Continue reading Introduction