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Sean Caroll in one of his videos namely "The Biggest Ideas in the Universe | 9. Fields" says "These colorful lines that we have drawn are the wave functions for different states the mode could be in and we would square them to get the probability of observing the mode to have that height." 47:48 "All of the modes will have the property that there is very little probability of ever measuring the mode to have too much height..."

I would like to know how we measure the height (amplitude) of one particular mode. What do we get as a result of this measurement? Do we find out whether the mode is occupied or not?

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