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Waves and Uncertainty - Example 4

Quantum physics (or quantum mechanics) is a branch of physics which deals with physical phenomena where the action is on the order of the Planck constant. Quantum mechanics applies to a limited range of phenomena, including all matter with a positive integer spin, and many properties of atoms, molecules, solids, and subatomic particles. Some of these applications are readily understandable to the layperson, like the conductivity of semiconductors and the emission of light from atoms. Others, such as quantum computing and the uncertainty principle are less intuitive.

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Video Transcript

Welcome to our fourth example video in our section on particles, waves and uncertainty. This video will consider Heisenberg's uncertainty principle. Recall that we can write as Delta X Doubt PX must be greater than H bar over to so say, for example, that we want to find the possible range of momentum's for a for an object that we you know, it's position roughly two within 0.1. My Cron's okay, so that's 10 to the negative 7 m and we want to know what is the uncertainty within? What uncertainty can we figure out? P of x Delta p. X So we say we know here's our inequality, which means the uncertainty on our momentum measurement must be greater than must be greater than 1/0 0.1 times 10 to the negative 6 m multiplied by H bar over to recall that H bar is simply h divided by two pi. When we go ahead and type this in, then what we're going to have is 1/0 0.1 times 10 to the negative 6 m multiplied by 1.5 times 10 to the negative 34 Jules seconds, divided by to so plugging this endpoint one e to the negative six times 1.5 e to the negative 34 divided by two. What we end up with them is 5.25 Must be greater than or equal to 5.25 times 10 to the negative 28 kilograms meters per second. Now, Clearly, that's a very large number. And that's not the sort of range of units that were interested in any ways. We could convert this, say 2 g. We wanted to convert it to grams than we would have to multiply it by 1000 g for each kilogram. That would increase this order of magnitude. Same thing with changing from meters into nanometers. We'd end up getting a much smaller uncertainty than what we see here simply by changing the units. If you're worried about the number, but it's gonna be still the same exact value is what we see here. Remember, the same thing can be done with the uncertainty on energy and time, which will be of particular important as we start thinking more and more about the energy levels at which particles air living