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I think when it says "quantized or discrete" that discrete is just serving as a definition or qualifier for the word quantized. The difference between them is not the main point. When values are quantized they become discrete.
Quantized and discrete are intended to have the same definition here. It just means that the variables in a system has a only a number of distinct values it can be. For example, when we talk about principle energy levels, n, n can only equal to 1, 2, 3 or 4--never 1.2 or 2.4234, etc.
It is meant to draw notice to the fact that numbers in quantum equations cannot be "anything" like in a lot of classical mechanics situations. In lecture he used the example F= ma can have pretty much any number for each of those values, whereas in a quantum equation some variables will only be able to have specific values. (like 1,2,3,4...)
Doctor Lavelle used a very pertinent example of a water faucet in his discussion of the difference between discrete and quanta variables. Essentially, the holistic view of water exiting a water faucet is comparable to a discrete value because water is seen as continuously flowing. An example of this would be water traveling at a rate of 10 gallons per minute for 10 minutes; the rate is continuous. At a certain point, there were 5.4982097 gallons of water assuming the tub holding the water started at 0 gallons. However, if we scrutinize water on a molecular level, we see that water is really just comprised of water molecules. Water travels one water molecule at a time with no values in between because this would physically be impossible. This is comparable to a quanta variable. A helpful hint is that quanta means "quantity" and quantity should evoke a sense of whole numbers.
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