Forced harmonic oscillatorcanonical transformationquantization of the forced oscillatorIn this work we address the problem of the quantization of a simple harmonic oscillator that is perturbed by a time dependent force. The approach consists of reSocial Science Electronic Publishing...
= 0, then the Duffing equation describes a simple harmonic oscillator with linear damping (constant value of δ). Usually, when the Duffing equation or equation similar to it is analyzed, the values of δ, α, β and ξ are assumed to be constant. In such a case, the number of...
and we compare the derived circuit Hamiltonian with the quantum Rabi Hamiltonian, which describes a two-level system coupled to a harmonic oscillator. We show that there is a simple, intuitive correspondence between the circuit Hamiltonian
Do i need to substitute the general solution to the Lagrangian or i just have to substitute the homogeneous solution to the simple harmonic oscillator part and then substitute the general solution to the potential term the e(t)x. I'm really bothered regarding with this matter. Can someone ...
the discriminator output. The loop filter is fundamentally an integrator that accumulates the discriminator output to drive the error (discriminator output) to zero. The other module in the tracking loop is a numerically controlled oscillator (NCO). This is also a simple integrator, which ...
The results of the simple Thomas-Fermi model, in particular the approximate constancy of the c.m. quartetting potential in the core nucleus and the Thomas-Fermi rule, can be verified. However, the harmonic oscillator potential is not realistic for nuclei, especially near the surface of the ...
In the quantum region, the vibration of ion is described by a quantum harmonic oscillator that is written as 𝐻𝑅=ℏ𝜔𝑘𝑎†𝑎, where 𝜔𝑘 is the vibrational frequency and a (𝑎†) is the annihilation (creation) operator of phonons. Then, we have a general form of th...
The rope shovel is numerically represented as a rigid multi-body system where each body consists of several finite elements. Since rigid bodies were used, the mesh size is of little interest for all parts except the bucket. Dynamic behavior is applied through penalty-based joints. In Sect. ...
Analytical expressions for the spectral density of the tunnelling rate are found for a fission-like analytical barrier, having three parts: an internal part approximated by a harmonic oscillator, a top part considered constant and an external part considered as a Coulomb potential. We found that en...
The photonic structure consists of a micro-cavity like structure formed of two one-dimensional photonic crystals made of free-standing porous silicon, separated by a variable air gap and the working wavelength is 633 nm. We show experimental evidence of this force when the photonic structure is...