Is there a limit for passing of classical waves behind a slit? For the classical waves is there a limit for them to pass through a slit
when the dimentions of the slit are much smaller then the wavelength?
I think that the Hyugence principle must be valid and when the slit is
small then after the slit must evolve a pure concentric wave.
Is there any analytical solution which shows that when d->0 there are still
waves or otherwise that at some l/d (b.e.50) the waves dont propagate
after the slit. Is the situation similar for Schroedinger equation?
 A: In purely mathematical terms, one would observe diffraction for a slit of any width, if the corresponding equations (Maxwell equations, wave equation or whatever applies) are for continuous functions.
In practice, this is not the case:
The nature of waves
Wave equations are often derived in continuous limit, i.e., they apply only as long as the characteristic scales of their solutions (such as wave length) are much greater than the sizes of atoms/molecules, e.g., as in the case of equations of elasticity theory. Often the constraints are even harsher - e.g., the equations of hydrodynamics assume local equilibrium, that is the diffusion length and the relaxation time are much shorter than the characteristic length and time scales of the solution.
This is also true for Maxwell equations in media, since they similarly make an assumption of averaging magnetization and polarization over a physically small volume.
The nature of slits
Another aspect that one cannot neglect at small scales is the nature of the material of which the screen is made. Thus, one often assumes that the screen is either absorbing 100% of the waves incident on it or reflects 100% of them. This is however not true for any realistic material.
Thickness of the screen
Related to the previous question, if a screen is very thin, it is likely to be transparent to the waves. E.g., in case of electromagnetic waves, a non-transparent screen should be much thicker than the skin depth. This limits the size of the slits - if their width is smaller than the screen thickness, we need to consider whether the wave will be propagating within the slits and how it will be modified when it exits on the other side.
