Related papers: Adelic Model of Harmonic Oscillator
Using the Weyl quantization we formulate one-dimensional adelic quantum mechanics, which unifies and treats ordinary and $p$-adic quantum mechanics on an equal footing. As an illustration the corresponding harmonic oscillator is considered.…
The classical and quantum formalism for a p-adic and adelic harmonic oscillator with time-dependent frequency is developed, and general formulae for main theoretical quantities are obtained. In particular, the p-adic propagator is…
For the symmetric harmonic oscillator and the symmetric bouncer defined in 2-D, two different Hamiltonian are given describing the same classical dynamics; however, their quantum dynamics behavior are different.
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…
The harmonic oscillator is one of the most studied systems in Physics with a myriad of applications. One of the first problems solved in a Quantum Mechanics course is calculating the energy spectrum of the simple harmonic oscillator with…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
In this article we obtained the harmonic oscillator solution for quaternionic quantum mechanics ($\mathbbm{H}$QM) in the real Hilbert space, both in the analytic method and in the algebraic method. The quaternionic solutions have many…
An explicit solution of the equation for the classical harmonic oscillator with smooth switching of the frequency has been found . A detailed analysis of a quantum harmonic oscillator with such frequency has been done on the base of the…
Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding…
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…
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 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…
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in 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…
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master…
We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…
A certain notion of canonical equivalence in quantum mechanics is proposed. It is used to relate quantal systems with discrete ones. Discrete systems canonically equivalent to the celebrated harmonic oscillator as well as the quartic and…
A brief review of the previous research on the Heisenberg uncertainty relations at the Planck scale is given. In this work, investigation of the uncertainty principle extends to p-adic and adelic quantum mechanics. In particular, p-adic…
Problems concerning with application of quantum rules on classical phenomena have been widely studied, for which lifted up the idea about quantization and uncertainty principle. Energy quantization on classical example of simple harmonic…
We show that this problem gives rise to the same differential equation of a well known potential of ordinary quantum mechanics. However there is a subtle difference in the choice of the parameters of the hypergeometric function solving the…