Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in or
create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision |
Your text |
Line 13: |
Line 13: |
| </math> | | </math> |
| And again we get the same result. What do you think of it? Is there a mistake? Please help, I'm really stuck with it. [http://en.wikipedia.org/wiki/User:Yrogirg Grigory Sarnitskiy]. [[Special:Contributions/91.76.179.101|91.76.179.101]] 19:45, 30 January 2009 (CET) | | And again we get the same result. What do you think of it? Is there a mistake? Please help, I'm really stuck with it. [http://en.wikipedia.org/wiki/User:Yrogirg Grigory Sarnitskiy]. [[Special:Contributions/91.76.179.101|91.76.179.101]] 19:45, 30 January 2009 (CET) |
|
| |
| === A quick comment ===
| |
|
| |
| I may be wrong, but looking at your derivation it seems the boundary conditions are not correctly
| |
| described. If the system is fixed to some immobile frame, only <math>\sin</math> terms should appear in the modes, not <math>\cos</math>. If, on the other hand, periodic boundary conditions are applied, the opposite applies: only <math>\cos</math>, not <math>\sin</math>. This may explain the factor of <math>2</math> that's missing... but I still have to think more carefully about this. --[[User:Dduque|Dduque]] 09:58, 3 February 2009 (CET)
| |
| :Thank you. Yes, I didn't appreciate the importance of boundary conditions. I think it is quite reasonable to take something like <math>\frac{\partial h(x,y)}{\partial \mathbf{n}} \Big|_{wall}=0</math>, with <math>\mathbf{n}</math> normal to the wall. I suppose it is valid at least for more or less long waves (several minimal wavelengths), which contribute most to <math>\langle h \rangle</math>. It is likely there is no need to study molecular interaction between liquid and solid surface in this case — boundary conditions will not be affected by the material of the walls at least for real-life systems. So we get <math>\frac{1}{2} k_B T</math> for each mode. Still I'll think it over again and will wait for your reply. [[Special:Contributions/91.76.179.246|91.76.179.246]] 12:53, 3 February 2009 (CET) Well now I'm not sure at all in the variant above. Have to dig the question. [[Special:Contributions/91.76.179.246|91.76.179.246]] 15:29, 3 February 2009 (CET)
| |