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B Why does this term always approach 4?

  1. Nov 22, 2016 #1
    I have followed several derivations to obtain the formula for tunnelling probability in a finite square potential well.

    the standard result that is actually an approximation to a more complex result is;

    upload_2016-11-23_10-1-27.png

    I get the derivation of this result shown in many standard texts.

    what I do not get is the term before the exponential always approximates to the number 4.

    I am not interested in verifying this with actual values for V, E.

    I want to know algebraically why the term is always approximately equal to 4 for any values of V, E.

    it is supposed to be obvious and probably is, eludes me atm.

    authors often make a further approximation and ignore the entire term so they are always out by a factor of 4 on an already approximate answer.

    when dealing with such small numbers is leaving the 4 out that pedagogically sound - that's a seprate question.
     
  2. jcsd
  3. Nov 22, 2016 #2
    It certainly isn't close to 4 for "any" values. It's exactly 4 when V = 2 * E0. So I suppose there's some physical reason why V / E0 is usually close to 2. But I don't know why that would be.
     
  4. Nov 22, 2016 #3

    PeterDonis

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    Staff: Mentor

    Can you give some references that make this claim?
     
  5. Nov 23, 2016 #4
    not sure to be honest. will do a search.
     
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