houlahound
- 907
- 223
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;
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.
the standard result that is actually an approximation to a more complex result is;
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.