Finite square well potential question

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SUMMARY

The discussion focuses on determining the number of bound energy states for a finite one-dimensional square potential well with specific parameters: a proton mass of 1.67 x 10-27 kg, a well width of 2.0 fm, and a depth of 40 MeV. The energy levels are calculated using the formula En = (n2 * h2) /(8ma2), but it is crucial to note that this formula applies to infinite potential wells. To find the number of allowed energy states, one must consider the finite depth of the well and determine the maximum value of n for which the energy is less than 40 MeV.

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StephenD420
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For a finite one-dimensional square potential well if a proton is bound, how many bound energy states are there?

If m = 1.67*10^(-27) kg a = 2.0fm and the depth of the well is 40MeV.

Now I know the energy levels are
En = (n^2 * h^2) /(8ma^2) = (n^2*pi*2)/4 * (2hbar^2)/(ma^2)

but I am unsure as to how to find the number of the allowed energy states. Any help would be greatly appreciated.

Thanks.
Stephen
 
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Determine n belonging to the maximum magnitude of energy less then 40 MeV. But take care: the formula you cited refers to infinite potential wells. Here the potential well is of finite depth.

ehild
 
Last edited:

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