Related papers: Quaternionic quantum harmonic oscillator
A simple derivation of the classical solutions of a nonlinear model describing a harmonic oscillator on the sphere and the hyperbolic plane is presented in polar coordinates. These solutions are then related to those in cartesian…
We present a Lie algebraic approach to a Hamiltonian class covering driven, parametric quantum harmonic oscillators where the parameter set -- mass, frequency, driving strength, and parametric pumping -- is time-dependent. Our…
We show that a polynomial H(N) of degree N of a harmonic oscillator hamiltonian allows us to devise a fully solvable continuous quantum system for which the first N discrete energy eigenvalues can be chosen at will. In general such a choice…
We generalize a recently proposed algebraic method in order to treat non-Hermitian Hamiltonians. The approach is applied to several quadratic Hamiltonians studied earlier by other authors. Instead of solving the Schr\"odinger equation we…
A new approach to normal operators in real Hilbert spaces is discussed, and a spectral representation is obtained, derived directly from the complex case. The results are then applied to quaternionic normal operators, regarded as a special…
We use the Fourier operator to transform a time dependent mass quantum harmonic oscillator into a frequency dependent one. Then we use Lewis-Ermakov invariants to solve the Schr\"odinger equation by using squeeze operators. Finally we give…
We consider a quantum system consisting of a one-dimensional chain of M identical harmonic oscillators with natural frequency $\omega$, coupled by means of springs. Such systems have been studied before, and appear in various models. In…
The single well 1D harmonic oscillator is one of the most fundamental and commonly solved problems in quantum mechanics. Traditionally, in most introductory quantum mechanics textbooks, it is solved using either a power series method, which…
An infinite dimensional system such as a quantum harmonic oscillator offers a potentially unbounded Hilbert space for computation, but accessing and manipulating the entire state space requires a physically unrealistic amount of energy.…
By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
A relativistic quantum harmonic oscillator in 3+1 dimensions is derived from a quaternionic non-relativistic quantum harmonic oscillator. This quaternionic equation also yields the Klein-Gordon wave equation with a covariant (space-time…
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…
In a system of coupled harmonic oscillators, the interaction can be represented by a real, symmetric and positive definite interaction matrix. The quantization of a Hamiltonian describing such a system has been done in the canonical case.…
By means of numerical solutions of the quantum Hamilton Jacobi equation, a general WKB-like representation for one-dimensional wave functions is obtained. This representation is unique in the classically forbidden regions, while in the…
We briefly describe the construction of a consistent $q$-deformation of the quantum mechanical isotropic harmonic oscillator on ordinary $\rn^N$ space.
The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.
Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with…