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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.
[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 ...
To model both absorption and emission, one would need a jump operator for each. This leads to the most common Lindblad equation describing the damping of a quantum harmonic oscillator (representing e.g. a Fabry–Perot cavity) coupled to a thermal bath, with jump operators:
This is the partition function of one harmonic oscillator. Because, statistically, heat capacity, energy, and entropy of the solid are equally distributed among its atoms, we can work with this partition function to obtain those quantities and then simply multiply them by N ′ {\displaystyle N^{\prime }} to get the total.
The quantum harmonic oscillator; The quantum harmonic oscillator with an applied uniform field [1] The Inverse square root potential [2] The periodic potential The particle in a lattice; The particle in a lattice of finite length [3] The Pöschl–Teller potential; The quantum pendulum; The three-dimensional potentials The rotating system The ...
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 ...
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.
For example, a quantum harmonic oscillator may be in a state | for which the expectation value of the momentum, | ^ | , oscillates sinusoidally in time. One can then ask whether this sinusoidal oscillation should be reflected in the state vector | ψ {\displaystyle |\psi \rangle } , the momentum operator p ^ {\displaystyle {\hat {p}}} , or both.