This book contains detailed insights on the calculus of variations that
studies the equilibrium density matrix for many-particle Fermi systems. There
are two approximations taken into account in the book. The simplest one is the
mean field approximation. The second approximation applies not only to the
particle distribution pattern but also to the correlation function. The
variational principle for electron distribution function among wave vectors has
been denoted in the work.
The method that makes using the density matrix for finding the valence electron
energy in metal has been proposed. It has been proved that the Coulomb interaction
of electrons in a crystal lattice results in production of the model
Hamiltonian consisting of two components.
One component describes attraction of electrons with the equal wave
vectors inducing formation of specific electron pairs. The other component
describes repulsion of electrons with the wave vectors being equal by size and
opposite by direction. This component denotes the anisotropy regarding
distribution of electrons among wave vectors thus indicating the
superconducting substance ability.
The Fermi-Dirac distribution function, as considered together with the
model Hamiltonian, explains all the properties exhibited by superconductors.
Thus, the effect of a magnetic field on the superconducting states is studied
in the book.
The book can be interesting for senior schoolchildren, students of higher educational
institutions, postgraduates and teachers.