Improvement of Uncertainty Relations for Mixed States

Fuzzy relations, Possibility theory, Measures of uncertainty, Mathematical modeling.

A central aim of educational research in the area of mathematical modeling and applications is to recognize the attainment level of students at defined states of the modeling process. In this paper, we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modeling in the classroom. The main stages of the modeling process are represented as fuzz...

Cauchy Inequality and Uncertainty Relations for Mixed States

Rényi Entropy and the Uncertainty Relations

Quantum mechanical uncertainty relations for the position and the momentum and for the angle and the angular momentum are expressed in the form of inequalities involving the Rényi entropies. These uncertainty relations hold not only for pure but also for mixed states. Analogous uncertainty relations are valid also for a pair of complementary observables (the analogs of x and p) in N-level syste...

Remarks on the Extended Characteristic Uncertainty Relations

In the recent papers [1, 2] the conventional uncertainty relation (UR) of Robertson [5] (which includes the Heisenberg and Schrödinger UR [4] as its particular cases) have been extended to all characteristic coefficients of the uncertainty matrix [2] and to the case of several states [1]. In this letter we present three remarks on these extended characteristic URs. The first remark refers to th...

مطالعه نیمه‌کلاسیکی چند رابطه جابه‌جاگری تعمیم‌یافته

  Our aim in this paper is to find the observable effects of the generalized commutators. For this purpose we investigate two problems in quantum mechanics with minimal length procedure. Firstly, we study hydrogen atom energy levels via minimal length uncertainty relation algebra. From comparing our results, with experimental data we estimate an upper limit for minimal length. Secondly, we inve...