Comment on “Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty”

Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty

We study non-Hermitian quantummechanics in the presence of a minimal length. In particular we obtain exact solutions of a non-Hermitian displaced harmonic oscillator and the Swanson model with minimal length uncertainty. The spectrum in both the cases are found to be real. It is also shown that the models are η pseudo-Hermitian and the metric operator is found explicitly in both the cases.

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...

Minimal length in Quantum Mechanics and non-Hermitian Hamiltonian systems

Hermitian metric on quantum spheres

The paper deal with non-commutative geometry. The notion of quantumspheres was introduced by podles. Here we define the quantum hermitianmetric on the quantum spaces and find it for the quantum spheres.

Non-hermitian extensions of Schrödinger type uncertainty relations

In quantum mechanics it is well known that observables are represented by hermitian matrices (or operators). Uncertainty relations are represented as some kinds of trace inequalities satisfied by two observables and one density matrix (or operator). Now we try to release the hermitian restriction on observables. This is only a mathematical interest. In this case we give several non-hermitian ex...