Search results
Results from the WOW.Com Content Network
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point , it is one of the most important model systems in quantum mechanics.
Here ¯ is the mean number of excitations in the reservoir damping the oscillator and γ is the decay rate. To model the quantum harmonic oscillator Hamiltonian with frequency of the photons, we can add a further unitary evolution:
In physics, the fundamental solution, (Green's function), or propagator of the Hamiltonian for the quantum harmonic oscillator is called the Mehler kernel.It provides the fundamental solution [3] φ(x,t) to
[citation needed] A quantum Drude oscillator (QDO) [5] [6] [7] is a natural extension to the classical Drude oscillator. Instead of a classical point particle serving as a proxy for the charge distribution, a QDO uses a quantum harmonic oscillator, in the form of a pseudoelectron connected to an oppositely charged pseudonucleus by a harmonic ...
For the treatment of the quantum harmonic oscillator in quantum mechanics, it is replaced by the tensor-valued Fradkin operator. The Fradkin tensor provides enough conserved quantities to make the oscillator's equations of motion maximally superintegrable . [ 3 ]
Some expanded derivations and an example of the harmonic oscillator in the Heisenberg picture The original Heisenberg paper translated (although difficult to read, it contains an example for the anharmonic oscillator): Sources of Quantum mechanics B.L. Van Der Waerden [2]
A quantum bus is often implemented as a microwave cavity modeled by a quantum harmonic oscillator. Coupled qubits may be brought in and out of resonance with the bus and with each other, eliminating the nearest-neighbor limitation. Formalism describing coupling is cavity quantum electrodynamics.
The quantum harmonic oscillator (and hence the coherent states) arise in the quantum theory of a wide range of physical systems. [2] For instance, a coherent state describes the oscillating motion of a particle confined in a quadratic potential well (for an early reference, see e.g. Schiff's textbook [3]). The coherent state describes a state ...