Pseudo-Hermitian approach to energy-dependent Klein-Gordon models

The relativistic Klein-Gordon system is studied as an illustration of Quantum Mechanics using non-Hermitian operators as observables. A version of the model is considered containing a generic coordinate- and energy-dependent phenomenological mass-term $m^2(E,x)$. We show how similar systems may be assigned a pair of the linear, energy-independent left- and right-acting Hamiltonians with quasi-Hermiticity property and, hence, with the standard probabilistic interpretation.Comment: 2nd Int. Workshop "Pseudo-Hermitian Hamiltonians in Quantum Physics" (http://gemma.ujf.cas.cz/~znojil/conf

Emlakbank'tan Ahmet Özal'a takip

Taha Toros Arşivi, Dosya No: 47-Turgut ÖzalUnutma İstanbul projesi İstanbul Kalkınma Ajansı'nın 2016 yılı "Yenilikçi ve Yaratıcı İstanbul Mali Destek Programı" kapsamında desteklenmiştir. Proje No: TR10/16/YNY/010

Symmetry reductions for the Tzitzeica curve equation

The purpose of the paper is to analyze the Tzitzeica curve equation from the point of view of symmetry analysis theory. The Tzitzeica curve equation is a nonlinear ordinary differential equation that arises from differential geometry that may be regarded as a differential equation in three unknown functions, namely, the functions that give the parametrical representation of the curve. The extended classical symmetries, the generalized equivalence transformations and the equivalence transformations related to this nonlinear ordinary differential equation are determined

Symmetry reductions related to specific nonlinear models

The purpose of this work is to explore possible side conditions involving high order differential invariants with the aim of reducing the original mathematical model. It is shown that, in the case of the Tzitzeica curve equation, a suitable side condition that leads to exact solutions is a system consisting of two third order differential invariants involving the arbitrary functions and a third order differential invariant involving the dependent variable of the equation. In this situation, the equation can be reduced to a linear equation for the equation\u27s constant. Similarly, in the case of a proposed generalization of the Tzitzeica curve equation, the above side condition also leads to a reduced model

Analisis Kesalahan Siswa Dalam Menyelesaikan Soal Statistika MTs Kelas VIII

This study aims to analyze students' mistakes in completing statistical questions for class VIII, using qualitative descriptive research with the method of collecting data, and using test questions while the validity of the data by means of the test validity. This subject is 21 people. This research was conducted to students of class VIII Madrasah Tsanawiyah At-Taqwa West Bandung Regency academic year 2019/2020. The results of this study revealed that errors experienced by students varied including: 1) presenting statistical reports in the form of diagrams, either bar or circle diagrams; 2) determine the average value of a story and diagram problem; 3) determine the profit (%) by finding the average. While the error factors that can affect students in solving statistical material problems are: lack of initial understanding of the material about statistics, student motivation in following the teaching and learning process, learning with the model that is done is less motivating students to learn creatively and actively in understanding statistics subject matter