Relativistic solutions of generalized-Dunkl harmonic and anharmonic oscillators

Generalized Heisenberg relation and Quantum Harmonic Oscillators

We study the consequences of the generalized Heisenberg uncertainty relation which admits a minimal uncertainty in length such as the case in a theory of quantum gravity. In particular, the theory of quantum harmonic oscillators arising from such a generalized uncertainty relation is examined. We demonstrate that all the standard properties of the quantum harmonic oscillators prevail when we em...

The One-dimensional Thermal Properties for the Relativistic Harmonic Oscillators

The relativistic harmonic oscillator is one of the most important quantum system, as it is one of the very few that can be solved exactly. The Dirac relativistic oscillator (DO) interaction is an important potential both for theory and application. It was for the first time studied by Ito et al [1]. They considered a Dirac equation in which the momentum p is replaced by p − imβω r, with r being...

Specific heat, Energy Fluctuation and Entropy of Isotropic Harmonic and Anharmonic Oscillators

Exact solutions for a family of discretely spiked harmonic oscillators

5 Normalization and orthogonalization 15 5.1 Admissible physical solutions . . . . . . . . . . . . . . . . . . 16 5.2 Linear normalization . . . . . . . . . . . . . . . . . . . . . . . 16 5.3 Radial normalization . . . . . . . . . . . . . . . . . . . . . . . 18 5.3.1 One dimensional . . . . . . . . . . . . . . . . . . . . . 18 5.3.2 Two dimensional . . . . . . . . . . . . . . . . . . . . . 20 5...

Zeros of eigenfunctions of some anharmonic oscillators

where P is a real even polynomial with positive leading coefficient, which is called a potential. The boundary condition is equivalent to y ∈ L(R) in this case. It is well-known that the spectrum is discrete, and all eigenvalues λ are real and simple, see, for example [3, 14]. The spectrum can be arranged in an increasing sequence λ0 < λ1 < . . .. Eigenfunctions y are real entire functions of o...