Related papers: An analysis of states in the phase space: the anha…
This is the third article in a series of three papers on the resonance energy levels of anharmonic oscillators. Whereas the first two papers mainly dealt with double-well potentials and modifications thereof [see J. Zinn-Justin and U. D.…
We perform a study of various anharmonic potentials using a recently developed method. We calculate both the wave functions and the energy eigenvalues for the ground and first excited states of the quartic, sextic and octic potentials with…
The well-known algorithm for quantum phase estimation requires that the considered unitary is available as a conditional transformation depending on the quantum state of an ancilla register. We present an algorithm converting an unknown…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
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…
A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schr\"odinger…
A translation invariant system of interacting quantum anharmonic oscillators indexed by the elements of a simple cubic lattice $\mathbb{Z}^d$ is considered. The anharmonic potential is of general type, which in particular means that it…
We propose a model for the quantum harmonic oscillator on a discrete lattice which can be written in supersymmetric form, in contrast with the more direct discretization of the harmonic oscillator. Its ground state is easily found to be…
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.
In phase space, we analytically obtain the characteristic functions (CFs) of a forced harmonic oscillator [Talkner et al., Phys. Rev. E, 75, 050102 (2007)], a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz, Phys.…
Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical…
Rotationally invariant space with noncommutativity of coordinates and noncommutativity of momenta of canonical type is considered. A system of $N$ interacting harmonic oscillators in uniform filed and a system of $N$ particles with harmonic…
Given its well known spectral decomposition profile, the $1$-dim harmonic oscillator potential modified by an inverse square ($1$-dim angular momentum-like) contribution works as an efficient platform for probing classical and quantum…
We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems. The relevant uncertainty principle is…
The energy gap between the first excited state and the ground state is calculated for the quantized anharmonic oscillator in the framework of the functional renormalization group method. The compactly supported smooth regulator is used…
A new scheme of field quantization is proposed. Instead of associating with different frequencies different oscillators we begin with a single oscillator that can exist in a superposition of different frequencies. The idea is applied to the…
The frequency of a classical periodic system and the energy levels of the corresponding quantum system can both be obtained using action variables. We demonstrate the construction of two forms of the action variable for a one dimensional…
The energy levels of quantum systems are determined by quantization conditions. For one-dimensional anharmonic oscillators, one can transform the Schrodinger equation into a Riccati form, i.e., in terms of the logarithmic derivative of the…
Experimental results from literature show equidistant energy levels in thin Bi films on surfaces, suggesting a harmonic oscillator description. Yet this conclusion is by no means imperative, especially considering that any measurement only…
Evolution of coherent states is considered for a particle confined to a cylinder moving in a harmonic oscillator potential. Because of the discontinuous changes as time goes by of the phase representing the position of a particle on a…