- Why doesn't my energy come in discrete levels?
- Why is my position so easy to measure, and not spread out over the entire universe?
In 1991 issue of Physics Today, Zurek outlines an answer. As you look over his analysis, here are some of the concepts he discusses:
- The state |ψ> is what we, last time, referred to as the probability density of the particle's position. (Technically, you use |ψ> to calculate the probability density, and it can be rewritten as the probability density of any measurable quantity, but the simple explanation suffices for now.) The pointy shape | > that ψ is encased in is just a symbol that denotes what type of quantity it is (an infinite-dimensional vector of complex components, which is a member of a set called Hilbert space). Just think of it as a function--a very, very special function! (Long description here.)
- Spin-1/2 is related to what we discussed in our series about spintronics, that protons and electrons (and, therefore, atoms) have an inherent property whose equations look a lot like the particles are spinning. Because spin is a quantum mechanical property, it comes in discrete lumps, and for protons and electrons, the spin (as measured along a selected axis) can take on two values (in units of Planck's constant): +1/2 and -1/2. These values lead to the colloquial terms "spin-up" and "spin-down," and electron or proton spin is a "simple" problem to study, since the state |ψ> need only specify two numbers: α (the probability of the particle being spin-up) and β (the probability of the particle being spin-down).
The mathematics in Zurek's article can get a bit cumbersome, so if you're new to quantum mechanics, focus on his commentary! Have a question about a step he takes or what a symbol means? Post it in the comments below!
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