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The textbook explains the "particle in a box" concept and says "the idea to keep in mind is that only certain wavelengths can exist in the box." Can someone explain this further? Why is it called a "particle in a box" and how does it prove that only certain wavelengths can exist? Also, what does the "box" refer to?
The particle is being modeled as a wave, just like we modeled the electron as a wave. In class we discussed that for the wave model of the electron there had to be a whole wavelengths for it to be stable (refer to class notes on circular standing wave).
Basically think of what a wavelength is. It is the distance from one "peak" to another "peak." Think of a wavelength in a "box." It is bounded on 2 sides right? Therefore only a certain wavelength can "fit" into this box. A bigger or smaller wavelength will be discontinuous.
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