منابع مشابه
Operator and Spectral Theory
This lecture is a complete introduction to the general theory of operators on Hilbert spaces. We particularly focus on those tools that are essentials in Quantum Mechanics: unbounded operators, multiplication operators, self-adjointness, spectrum, functional calculus, spectral measures and von Neumann’s Spectral Theorem. 1.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . ...
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where γj are selfadjoint 4× 4matrices satisfying the relations (2) γjγl + γlγj = 2δl,j . Obviously, if the domain of D0 is defined asH1(R3;C4), then D0 is a selfadjoint operator in L2(R3;C4). The spectrum of D0 is absolutely continuous, it coincides with the complement of the interval (−1, 1) as a set: σ(D0) = σa.c.(D0) = (−∞,−1] ∪ [1,∞). The multiplicity of the spectrum is infinite. We see tha...
متن کاملThe Spectral Shift Operator
We introduce the concept of a spectral shift operator and use it to derive Krein's spectral shift function for pairs of self-adjoint operators. Our principal tools are operator-valued Herglotz functions and their logarithms. Applications to Krein's trace formula and to the Birman-Solomyak spectral averaging formula are discussed.
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We consider Jacobi matrices with zero diagonal and off-diagonals given by elements of the hull of the Fibonacci sequence and show that the spectrum has zero Lebesgue measure and all spectral measures are purely singular continuous. In addition, if the two hopping parameters are distinct but sufficiently close to each other, we show that the spectrum is a dynamically defined Cantor set, which ha...
متن کاملThe Microscopic Dirac Operator Spectrum
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1968
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1968-0225192-0