Born-Von Karman boundary conditions

[no_math_plz]

I can't understand this conditions, and in general every boundary conditions for problems like this. they states "the choice of boundary conditions can be determined by mathematical convenience (!?) ... for if the metal is sufficiently large, we should expect its bulk properties not to be affected by the detailed configuration of surface" I'm a bit confused. from where they derive? from some postulates? doesn't exist postulates in quantum mechanics concerning boudary conditions. can you help me?

 

[olgranpappy]

For example, in the first QM problem you ever solved (the particle in a box) the boundary conditions were given to you: $\psi(0)=\psi(L)=0$, where L is the size of the box. These conditions are physical since the particle can't be outside the box.

You could, however, solve the problem with periodic boundary conditions instead of the physical boundary condition if you like and you will find only "half as many" solutions which you would then account for by saying that the wave vector can be taken as positive or negative, etc etc etc. And, presumably, when you calculate something like the density and take the limit as $L\to\infty$ you obtain the same result regardless of boundary conditions.

 

[no_math_plz]

for a particle in a box I have more solutions (twice) because I ignore boundary conditions for first derivative! I must take account of these conditions because a Bloch electron can't be localized, is a running electron. I can't say "electron is in a volume V", I think it has no sense. So, what's the role of V? Please, if I wasn't so clear, plaese make me notice it. Maybe I've an idea to resolve this problem, but I would like to know what do you think about my considerations first