Finite square well potential question

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In a finite one-dimensional square potential well, the number of bound energy states for a proton can be determined by analyzing the energy levels in relation to the well's depth. The energy levels formula provided is applicable to infinite potential wells, so adjustments must be made for finite wells. To find the maximum allowed quantum number n, one must ensure that the calculated energy levels remain below the well's depth of 40 MeV. The discussion emphasizes the importance of using the correct approach for finite potential wells to accurately determine the number of bound states. Understanding these principles is crucial for solving problems related to quantum mechanics and potential wells.
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
 
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