The Born Von Karman Boundary Conditions

[Llewlyn]

Hi to all community of Physic's help from Florence,

looking at born-von karman BC I'm a bit confused. I put this condition when i assume periodicity of wave function where the period is the spatial dimension of my system. I found that BC first in solid state physic, then I've noticed that became the natural BC for "all" quantum system.
I don't understand what i physically say.

It's not obvious (to me) that a wavefunction must have some symmetriy (although it's a bit intuitive). My "state of matter lectures" said:

"We can think at nullify wavefunction out of crystal as possible BC. This condition brings stationary solutions while we need progressive waves for describing phenomena like energy or charge transport".

...and so we use the born von-karman.

Its really sounds obscure to me

Ll.

 

[olgranpappy]

The point is that the bulk physics doesn't depend on the boundary conditions, so we can use whatever boundary conditions we please. Of course, if we are interested in surface effects, we can not use periodic boundary conditions.

To show explicitly that the bulk physics doesn't care about the existence of walls located very far away is not actually too easy, but the idea is easy to understand and somewhat "obvious."

Some rather famous physicists (Raman, for example) have also asked this question about periodic boundary conditions--and the definitive answer has always been given by Peierls (see, for example, his book "surprises in theoretical physics" or his paper he wrote in response to Raman's questions... I can't remember the reference at the moment, sorry.)

 

[Llewlyn]

Dear olgranpappy,

i really thank you for your answer.
This morning I've looked the Pierels book and I've found what u mean at chapter 3.6. He accepts intuitively that the bulk physics is unchanged because linear dimensions are huge than atomic scales. Then he proofs how surface effect influences wave function and he use it as error when u put periodic BC.
I think i should stop my research at this point, thank you again.

Ll.

 

[olgranpappy]

Dear olgranpappy,

i really thank you for your answer.
This morning I've looked the Pierels book and I've found what u mean at chapter 3.6. He accepts intuitively that the bulk physics is unchanged because linear dimensions are huge than atomic scales. Then he proofs how surface effect influences wave function and he use it as error when u put periodic BC.
I think i should stop my research at this point, thank you again.

Ll.

You're very welcome. Have fun with your studies.

 

[dub574]

thanks for the pointer olgranpappy, much appreciated