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.
What links here; Upload file; Special pages; Printable version; Page information
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 ...
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:
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 ]
(Sections I to IV of this article provide an overview over the Wigner–Weyl transform, the Wigner quasiprobability distribution, the phase space formulation of quantum mechanics and the example of the quantum harmonic oscillator.) "Weyl quantization", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Terence Tao's 2012 notes on Weyl ordering
For example, a quantum harmonic oscillator may be in a state |ψ 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 , the momentum operator p ^ {\displaystyle {\hat {p}}} , or both.
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