Related papers: Instanton solutions on the polymer harmonic oscill…
Controlled time-decaying harmonic potentials decelerate the velocity of the charged particle but the particle never be trapped by this harmonic potentials. This physical phenomena changes threshold between the short range class of potential…
We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal…
We show that the unitary evolution of a harmonic oscillator coupled to a two-level system can be undone by a suitable manipulation of the two-level system -- more specifically: by a quasi-instantaneous phase change. This enables us to…
We devise an efficient scheme to determine vibrational properties from Path Integral Molecular Dynamics (PIMD) simulations. The method is based on zero-time Kubo-transformed correlation functions and captures the anharmonicity of the…
The Hamiltonian of the harmonic oscillator is usually defined as a differential operator, but an integral representation can be obtained by using the coherent state quantization. The finite frame quantization is a finite counterpart of the…
We study the eigenvalue problem $-u"+V(z)u=\lambda u$ in the complex plane with the boundary condition that $u(z)$ decays to zero as $z$ tends to infinity along the two rays $\arg z=-\frac{\pi}{2} \pm \frac{2\pi}{m+2}$, where…
We compute the particle creation of a harmonic oscillator using the classical stochastic method. This recently constructed method reproduces all the vacuum expectation values in quantum theory. We prepare the vacuum state at the initial…
Enlightened by Lemma 1.7 in \cite{LiangLuo2021}, we prove a similar lemma which is based upon oscillatory integrals and Langer's turning point theory. From it we show that the Schr{\"o}dinger equation $${\rm i}\partial_t u = -\partial_x^2…
Instanton -- antiinstanton pair is considered as a source of singularity at the Borel plane for the ground state energy of anharmonic oscillator. The problem of defining the short range instanton -- antiinstanton interaction reduces to…
The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum $l$. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically…
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 introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…
We consider the relations between nonstationary quantum oscillators and their stationary counterpart in view of their applicability to study particles in electromagnetic traps. We develop a consistent model of quantum oscillators with…
In this chapter we treat the quantum damped harmonic oscillator, and study mathematical structure of the model, and construct general solution with any initial condition, and give a quantum counterpart in the case of taking coherent state…
We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. {\bf 62}, 092101 (2021)] in the classical and quantum formalisms, by introducing the effect of the mass function in both kinetic…
We construct Green's function for the quantum degenerate parametric oscillator in terms of standard solutions of Ince's equation in a framework of a general approach to harmonic oscillators. Exact time-dependent wave functions and their…
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 report that upon excitation by a single pulse, the classical harmonic oscillator immersed in classical electromagnetic zero-point radiation, as described by random electrodynamics, exhibits a quantized excitation spectrum in agreement to…
We consider the Dirac equation with a generalized uncertainty principle in the presence of the Harmonic interaction and an external magnetic field. By doing the study in the momentum space, the problem solved in an exact analytical manner…
We consider a radiation from a uniformly accelerating harmonic oscillator whose minimal coupling to the scalar field changes suddenly. The exact time evolutions of the quantum operators are given in terms of a classical solution of a forced…