- #1
- 2,810
- 605
In some parts of the physics,sometimes it happens that the volume of a region of space or the area of a surface enters into a formula.In such situations,most of the time,the author argues that "although I have derived this formula for such a shape,it is independent of the shape of the region/surface". For example the formula for Fermi energy.In textbooks a cube is considered for the proof but at the end,the volume is simply put there and every one seems to be fine with it.
Now I can imagine only two possibilities:
1-The author(or any other physicist)knows a proof which doesn't need any assumption about the shape.
2-There is a general theorem which says any formula proved for a particular shape,is true for all shapes!
I know the 2nd possibility seems weird,but well...Its not that unreasonable to be impossible!
Anyway,I want to know if the first possibility is correct, are those proofs published in books as the ones dependent on the shape?
And if the second possibility is correct,I'm just longing to know about that magical theorem!
Thanks
Now I can imagine only two possibilities:
1-The author(or any other physicist)knows a proof which doesn't need any assumption about the shape.
2-There is a general theorem which says any formula proved for a particular shape,is true for all shapes!
I know the 2nd possibility seems weird,but well...Its not that unreasonable to be impossible!
Anyway,I want to know if the first possibility is correct, are those proofs published in books as the ones dependent on the shape?
And if the second possibility is correct,I'm just longing to know about that magical theorem!
Thanks