Unitary Transformations in Solid State Physics
The main emphasis of this book is on the practical application of unitary transformations to problems in solid state physics. This is a method used by the author and his collaborators for years in the field of nonadiabatic electron-phonon phenomena where the Born-Oppenheimer approximation is no longer applicable. This book is intended as a tool for those who want to apply unitary transformations quickly and on a more elementary level and also for those who want to use this method for more involved problems. Unitary Transformations in Solid State Physics'' is divided into 6 chapters. The first three chapters are concerned with presenting quick applications of unitary transformations and chapter 4 presents a more systematic procedure. The last two chapters contain the major known examples of the utilization of unitary transformations in solid state physics, including such highlights as the Frohlich and the Fulton-Gouterman transformations. The book is supplemented by extended tables of unitary transformations, whose properties and peculiarities are also listed.
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Simple and standard transformation forms
Single spin transformations
Harmonically coupled oscillators
36 other sections not shown
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2-level 2nd order Abbreviations adiabatic adiabatic base anharmonic Ansatz approximation Bogoliubov transformation Bose calculation choice coefficients Comments commutation relations commutator expansion consider coordinates correlation functions coupling denotes Diagonalization Number dynamics eigenfunctions eigenvalue eigenvectors electron-phonon electronic subsystem energy exciton exp5 expansion 5.1 expectation value exponential expression expS S+ expS S+--S Formulae frequency Frohlich ft2+ given Green functions Hermitian infinite phase factor Inserting interaction introduce Invariants Jahn-Teller lattice Linear transformation matrix means of eq minus sign mode moving base nondiagonal notation Number 12 Number 21 order diagonalization orthogonal orthonormality oscillator parameter perturbation theory phonon problem procedure properties real T:A requirement respect Schrodinger sinh solution Special form spin Suitability superconductivity T:A*U+AU test-Hamiltonian tion transformation exponent transformed Hamiltonian reads transition U-expS S+ U+AU T:*-U+ unitary operator unitary transformation vectors vibrational vibronic Wagner Wannier functions whence Xreal yields
Theory of Superconductivity: From Weak to Strong Coupling
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