Hermite functions and special Hermite functions  depending on Heisenberg group (ℍⁿ )

دوال هرميت ودوال هرميت الخاصة اعتماداً على زمرة هايزنبرغ (ℍⁿ)

المؤلفون

  • Soha Ali Salamah

الكلمات المفتاحية:

زمرة هايزنبرغ
تمثيلات شرودنجر
تحويل فورييه_ ويغنر
دوال هرميت
دوال هرميت الخاصة
ℍⁿ

الملخص

In this paper, we talk about Heisenberg group, the most known example from the lie groups. After that, we talk about the representation theory of this group, and the relationship between the representation theory of the Heisenberg group and the position and momentum operator and momentum operators (ors). relationship between the representation theory of the Heisenberg group and the position and momentum, that shows how we will make the connection between the Heisenberg group and physics.

Then we introduce and study some properties of the Hermite and special Hermite functions. These functions are eigenfunctions of the Hermite and special Hermite operators, respectively. The Hermite operator is often called the harmonic oscillator and the special Hermite operator is sometimes called the twisted Laplacian. As we will later see, the two operators are directly related to the sub-laplacian on the Heisenberg group. The theory of Hermite and special Hermite expansions is intimately connected to the harmonic analysis on the Heisenberg group. They play an important role in our understanding of several problems on ℍⁿ .

السيرة الشخصية للمؤلف

Soha Ali Salamah

 

Faculty of Sciences ||  Al-Baath University ||  Syria

التنزيلات

منشور

2020-06-30

كيفية الاقتباس

1.
Soha Ali Salamah. Hermite functions and special Hermite functions  depending on Heisenberg group (ℍⁿ ): دوال هرميت ودوال هرميت الخاصة اعتماداً على زمرة هايزنبرغ (ℍⁿ) . jnslas [انترنت]. 30 يونيو، 2020 [وثق 6 ديسمبر، 2021];4(2):41-30. موجود في: https://journals.ajsrp.com/index.php/jnslas/article/view/2628

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