A question regarding finite potential wells

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The discussion centers on the behavior of wave functions in finite potential wells, specifically comparing them to infinite potential wells. Users inquire about the characteristics of wave functions in a finite potential well that transitions from infinite potential to a linearly increasing potential. It is established that bound states can exist in finite potential wells, with wave functions extending into the potential region and damping rapidly to zero. The specifics of wave function behavior, including wavelength and damping characteristics, are critical for understanding energy states in these systems.

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Hi guys! This is my first post on Physics Forums even, and I have a question regarding potential wells with finite potential. I understand the infinite potential well but what if the well is finite? For example, if we a potential well with infinite potential to the left of 0, but with increasing potential (say linear with respect to x for simplicity) to the right, what would the waves look like for the different energy states? Are there even bound states or is it completely unbound? I'm having trouble thinking about this. Thanks in advance!
 
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The "wave" extends slightly into the areas of finite potential, but damp rapidly to 0.
 
Hi HallsofIvy. Thanks for the response. Could you be a little more specific on what the "extension" looks like? For the lowest energy state for example, would the wave just undergo half an oscillation then damp to zero? How could we determine wavelength, or the damping, etc. given an increasing potential?
 

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