Related papers: The Harmonic Oscillator in Quantum Mechanics: A Th…
A linear quantum harmonic oscillator factors into one dimensional oscillators and can be solved using creation and annihilation operators. We consider a spherical analogue. This analogue does not factor. The two dimensional case is…
The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
The equilibrium properties of an open harmonic oscillator are considered in three steps: First the creation and destruction operators are generalized for open dynamics and the creation operator is used to construct coherent states. The…
The ladder operators in harmonic oscillator are a well-known strong tool for various problems in physics. In the same sense, it is sometimes expected to handle the problems of repulsive harmonic oscillator in a similar way to the ladder…
A nonlinear model representing the quantum harmonic oscillator on the three-dimensional spherical and hyperbolic spaces, $S_\k^3$ ($\kappa>0$) and $H_k^3$ ($\kappa<0$), is studied. The curvature $\k$ is considered as a parameter and then…
The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to…
We study some fundamental issues related to the Hilbert space representation of quantum mechanics in the presence of a minimal length and maximal momentum. In this framework, the maximally localized states and quasi-position representation…
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…
In this note, we study the potential algebra for several models arising out of quantum mechanics with generalized uncertainty principle. We first show that the eigenvalue equation corresponding to the momentum-space Hamiltonian…
Using the technique of tridiagonal representation approach; for the first time, we extend this method to study quantum systems with literally perturbed Hamiltonians. Specifically, we consider a quantum system in a 3D spherical oscillator…
We consider algebras underlying Hilbert spaces used by quantum information algorithms. We show how one can arrive at equations on such algebras which define n-dimensional Hilbert space subspaces which in turn can simulate quantum systems on…
A generalized harmonic oscillator on noncommutative spaces is considered. Dynamical symmetries and physical equivalence of noncommutative systems with the same energy spectrum are investigated and discussed. General solutions of…
We describe quantum behaviors of a simple harmonic oscillator, starting from the classical mechanics. By imposing two conditions on the phase points generated from a symplectic algorithm, we obtain discrete energy levels, satisfying $E_n…
We study quantum decoherence numerically in a system consisting of a relativistic quantum field theory coupled to a measuring device that is itself coupled to an environment. The measuring device and environment are treated as quantum,…
The one-dimensional Schr\"{o}dinger equation with the singular harmonic oscillator is investigated. The Hermiticity of the operators related to observable physical quantities is used as a criterion to show that the attractive or repulsive…
The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic…
Canonical quantization has taught us great things. A common example is that of the harmonic oscillator, which is like swinging a ball on a string back and forth. However, the half-harmonic oscillator blocks the ball at the bottom and then…
We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
We propose a q-deformation of the su(2)-invariant Schrodinger equation of a spinless particle in a central potential, which allows us not only to determine a deformed spectrum and the corresponding eigenstates, as in other approaches, but…