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Katedra Metod Matematycznych Fizyki (KMMF) Wydziału Fizyki UW: tematyka, ludzie, historia

Wojtkiewicz Jacek

Postępy Fizyki

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2022

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T. 73, z. 3

2--10

PL

Artykuł ten jest pomyślany jako uzupełnienie wspomnień zamieszczonych w [1], poświęconych genezie i rozwojowi Katedry Metod Matematycznych Fizyki WF UW. Zamierzam przede wszystkim przedstawić główne nurty badań, prowadzonych w Katedrze. Nie będę też jednak stronić od aspektów historycznych z naciskiem na lata bardziej współczesne niż w [1]. Zamierzam również poczynić kilka uwag na temat związków między fizyką a matematyką.

EN

The aim of this article is continuation of memoirs devoted to the emergence and development of the Department for Mathematical Methods in Physics [1]. The main subject of the present article is presentation of directions of research performed in the Department. I will also present some historic aspects of the Department, complementing the story told in [1]. I will also put few remarks concerning connections and interrelations between mathematics and physics.

2

Application of imaging visibility to measurement of correlation coefficient of scattering potential

Liu H., Wang W., Liu J., Liu W.

Optica Applicata

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2011

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Vol. 41, nr 3

557--565

EN

It is shown that the imaging visibility of intensity correlated scattered field may be utilized to determine the normalized correlation coefficient of the scattering potential (CCSP) of the quasi-homogeneous (QH) media illuminated by a scalar plane wave. The relationship between the imaging visibility and the CCSP is constructed by analytical forms. As long as the visibility of the intensity correlated scattered field is known, the scaled width of the CCSP can be expressed by solutions of the inverse scattering problem.

3

Geometric properties of quantum graphs and vertex scattering matrices

Kurasov P., Nowaczyk M.

Opuscula Mathematica

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2010

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Vol. 30, no. 3

295-309

EN

Differential operators on metric graphs are investigated. It is proven that vertex matching (boundary) conditions can be successfully parameterized by the vertex scattering matrix. Two new families of matching conditions are investigated: hyperplanar Neumann and hyperplanar Dirichlet conditions. Using trace formula it is shown that the spectrum of the Laplace operator determines certain geometric properties of the underlying graph.

4

Well-Posed Linear Systems - a Survey With Emphasis on Conservative Systems

Weiss G., Staffans O. J., Tucsnak M.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 1

7-33

EN

We survey the literature on well-posed linear systems, which has been an area of rapid development in recent years. We examine the particular subclass of conservative systems and its connections to scattering theory. We study some transformations of well-posed systems, namely duality and time-flow inversion, and their effect on the transfer function and the generating operators. We describe a simple way to generate conservative systems via a second-order differential equation in a Hilbert space. We give results about the stability, controllability and observability of such conservative systems and illustrate these with a system modeling a controlled beam.

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The J-matrix method: numerical computations

Syty P.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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1999

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Vol. 3, No 3

269-276

EN

Numerical calculations of scattering phase shifts have been done using J-matrix method (both non-relativistic and relativistic versions). Results of computations for some simple potentials are described and discussed in this paper. In particularly, it has been shown, that successive numerical approximations converge to results obtained using an analytical formula.