The new theoretical approach is proposed for studying the coupled states responsible for superconductivity in crystal without using the idea of electron pairing. From our approach it follows that BCS electron-pairing postulates are only approximate. It is shown that superconductivity (SC) coupled states can be created by pairs of electrons with nonzero full momentum and spin (k1 + k2 ≠ 0, s + s' ≠ 0). The model numerical calculations have shown that dependence of SC gap (energy of coupled states) on temperature is nonexponential and depends on the momenta of electrons in pair.
A theory is derived suitable to obtain t h e energy-momentum dependence for an arbitrarily coupling polaron. Using a variational principle general expressions are given which describe this dependence when a n arbitrary shape of the electron surface of constant energy is considered and the polarization field is approximated by any number of fictitious particles. This method is able t o yield the lowest band of electrons interacting with any mode of lattice vibrations. I n particular, numerical results for the energy, depending on the total momentum, are obtained for isotropic optical and piezoelectric polarons in a wide range of a dimensionless coupling constant. Comparison of the results with known ones (only weak and strong-coupling limits were investigated earlier) shows, that the energy values presented lie lower, though they represent themselves an upper bound for the exact polaron energymomentum relation.
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