[Turkmath:8662] MSGSÜ Genel Seminer (30 Kasım)

[Ayse Berkman]

*Mimar Sinan Güzel Sanatlar Üniversitesi *
*Matematik Bölümü Genel Semineri*

*Heun Functions and Their Uses in Physics*

Mahmut Hortaçsu  (MSGSÜ Fizik Bölümü)

Abstract: Most of the theoretical physics known today is described by using
a
small number of differential equations. If we study only linear systems,
different
forms of the hypergeometric or the confluent hypergeometric equations often
suffice
to describe this problem. These equations have power series solutions with
simple
relations between consecutive coefficients and can be generally represented
in terms
of simple integral transforms. If the problem is nonlinear, one often uses
one form
of the Painlevé equation. There are important examples, however, where one
has to use
more complicated equations. An example often encountered in quantum
mechanics is the
hydrogen atom in an external electric field, the Stark effect. One often
bypasses
this difficulty by studying this problem using perturbation methods. If one
studies
certain problems in astronomy or general relativity, encounter with the
Heun equation
is inevitable. This is a general equation whose special forms take names as
Mathieu,
Lamé and Coulomb spheroidal equations. Here the coefficients in a power
series expansions
do not have two way recursion relations. We have a relation at least
between three or
four different coefficients. A simple integral transform solution also is
not obtainable.
Here I will try to introduce this equation whose popularity increased
recently, mostly
among theoretical physicists, and give some examples where the result can
be expressed
in terms of solutions of this equation.

Tarih ve saat: 30 Kasım 2012 Cuma, 16.00

Yer: MSGSÜ Matematik Bölümü, Seminer Odası

Adres ve harita: http://mat.msgsu.edu.tr/iletisim.html

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Not: Her Cuma genel seminerimizden önce saat 14.30'da ayrıca bölüm içi
semineri yapmaktayız. Program için lütfen
http://mat.msgsu.edu.tr/Etkinlikler/bolum.html
sayfasına bakınız. İlgilenen herkes tüm seminerlerimize davetlidir.
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