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Titlebook: Mathematical Results in Quantum Mechanics; QMath7 Conference, P Jaroslav Dittrich,Pavel Exner,Miloš Tater Conference proceedings 1999 Sprin

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书目名称Mathematical Results in Quantum Mechanics
副标题QMath7 Conference, P
编辑Jaroslav Dittrich,Pavel Exner,Miloš Tater
视频video
丛书名称Operator Theory: Advances and Applications
图书封面Titlebook: Mathematical Results in Quantum Mechanics; QMath7 Conference, P Jaroslav Dittrich,Pavel Exner,Miloš Tater Conference proceedings 1999 Sprin
描述At the age of almost three quarters of a century, quantum mechanics is by all accounts a mature theory. There were times when it seemed that it had borne its best fruit already and would give way to investigation of deeper levels of matter. Today this sounds like rash thinking. Modern experimental techniques have led to discoveries of numerous new quantum effects in solid state, optics and elsewhere. Quantum mechanics is thus gradually becoming a basis for many branches of applied physics, in this way entering our everyday life. While the dynamic laws of quantum mechanics are well known, a proper theoretical understanding requires methods which would allow us to de­ rive the abundance of observed quantum effects from the first principles. In many cases the rich structure hidden in the Schr6dinger equation can be revealed only using sophisticated tools. This constitutes a motivation to investigate rigorous methods which yield mathematically well-founded properties of quantum systems.
出版日期Conference proceedings 1999
关键词Analysis; Mathematical physics; Potential; quantum mechanics; scattering theory
版次1
doihttps://doi.org/10.1007/978-3-0348-8745-8
isbn_softcover978-3-0348-9754-9
isbn_ebook978-3-0348-8745-8Series ISSN 0255-0156 Series E-ISSN 2296-4878
issn_series 0255-0156
copyrightSpringer Basel AG 1999
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https://doi.org/10.1007/978-3-0348-8745-8Analysis; Mathematical physics; Potential; quantum mechanics; scattering theory
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Mathematical Results in Quantum Mechanics978-3-0348-8745-8Series ISSN 0255-0156 Series E-ISSN 2296-4878
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The Spectral Shift OperatorWe 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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