Related papers: Exact Quantized Momentum Eigenvalues and Eigenstat…
Doplicher, Fredenhagen, and Roberts (1994, 1995) proposed a simple model of a particle in quantum spacetime. We give a new formulation of the model and propose some small changes and additions which improve the physical interpretation. In…
Gyratonic plane fronted gravitational waves are exact solutions of Einstein's field equations, which correspond to gravitational waves that carry momentum and angular-momentum. Using the definitions of the Hamiltonian formulation of the…
Bound states of the generalized spiked harmonic oscillator potential are calculated accurately by using the generalized pseudospectral method. Energy eigenvalues, various expectation values, radial densities are obtained through a…
In a recent paper by Jafarov, Nagiyev, Oste and Van der Jeugt (2020 {\sl J.\ Phys.\ A} {\bf 53} 485301), a confined model of the non-relativistic quantum harmonic oscillator, where the effective mass and the angular frequency are dependent…
We establish the correspondence between two apparently unrelated but in fact complementary approaches of a relativistic deformed kinematics: the geometric properties of momentum space and the loss of absolute locality in canonical…
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of…
In this study, we employ exact quantization rule (EQR) to derive the analytical approximate l-wave solutions of the Schrodinger equation with the general molecular oscillator (GMO). The energy eigenvalues equation and the corresponding wave…
In this article we have developed a formalism to obtain the Schr$\ddot{\rm{o}}$dinger equation for a particle in a frame undergoing an uniform acceleration in an otherwise flat Minkowski space-time geometry. We have presented an exact…
An alternative quantization rule, in which time becomes a self-adjoint operator and position is a parameter, was proposed by Dias and Parisio [Phys. Rev. A {\bf 95}, 032133 (2017)]. In this approach, the authors derive a…
This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…
We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by $$\mathcal H_N = p_1^2 + p_2^2 +\sum_{n=1}^N \gamma_n(q_1 p_1 + q_2 p_2)^n ,$$ where $q_i$ and $p_i$ are generic canonical variables, $\gamma_n$…
Accurate ro-vibrational energies, eigenfunctions, radial densities, expectation values are presented for the exponential-type Manning-Rosen (MR) potential. Bound states accurate up to ten significant figure are obtained by employing a…
Exact solutions of time-dependent Schr\"odinger equation in presence of time-dependent potential is defined by point transformation and separation of variables. Energy and Heisenberg uncertainty relation are pursued for time-independent…
A strengthened canonical quantization scheme for the constrained motion on a curved hypersurface is proposed with introduction of the second category of fundamental commutation relations between Hamiltonian and positions/momenta, whereas…
Dynamic equations concerning physical expectation values have been examined in terms of the real Hilbert space approach to quantum mechanics. The considered cases involve complex wave functions, as well as quaternionic wave functions. The…
Discussed is the quantized version of the classical description of collective and internal affine modes as developed in Part I. We perform the Schr\"odinger quantization and reduce effectively the quantized problem from $n^{2}$ to $n$…
Inspired by the recent work of Filho et al., a Hermitian momentum operator is introduced in a general curved space with diagonal metric. The modified Hamiltonian associated with this new momentum is calculated and discussed. Furthermore,…
We adopt the general formalism for analyzing evolution of gaussian states of quantized fields in time-dependent backgrounds in the Schrodinger picture (presented in detail in arXiv:0708.1233 and 0708.1237) to study the example of a…
Approximate analytical bound state solutions of the radial Schr\"odinger equation are studied for a two-term diatomic molecular potential in terms of the hypergeometric functions for the cases where $q\geq1$ and $q=0$. The energy…
The quantum resonances (QRs) of the kicked particle are studied in a most general framework by also considering {\em arbitrary} periodic kicking potentials. It is shown that QR can arise, in general, for {\em any rational} value of the…