First of all, the eigenfunction is a problem for me. The books I have do not describe the function whatsoever(!), does anyone understand it?

 

Secondly, is Schrodigner's equation only for the electron or for any particle?

1) Do you know linear algebra? A matrix can be seen as a linear map of a vector space on itself. An Eigenvector is a vector that remains the same under that transformation except for some scaling constant. The same holds true in QM. This time, your vector space is the so-called Hilbert Space, a space of functions. An operator is a map of this function space on itself. An Eigenfunction is a function that is mapped on itself under application of this operator (again: Except for some constant called "Eigenvalue").

2) The Schroedinger equations is the movement equation for any nonrelativistic quantum mechanical system. Note, however, that the appearing operator H (called the "Hamiltonian") differs from system to system.

First of all, the eigenfunction is a problem for me. The books I have do not describe the function whatsoever(!), does anyone understand it?

 

When you're talking about Schroedinger's equation, the wave function is the eigenfunction of the equation Hw=Ew, where w is the wave function, H is the hamiltonian, and E are the energy levels. H is the operator, the set of E's are the eigenvalues, and w is the eigenfunction.

 

Secondly, is Schrodigner's equation only for the electron or for any particle?

 

Nope, there are a bunch...Dirac's equation describes relativistic spin-1/2 particles (such as electrons).