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An oscillator that is not oscillating in harmonic motion is known as an anharmonic oscillator where the system can be approximated to a harmonic oscillator and the anharmonicity can be calculated using perturbation theory. If the anharmonicity is large, then other numerical techniques have to be used.
Implicit perturbation theory [13] works with the complete Hamiltonian from the very beginning and never specifies a perturbation operator as such. Møller–Plesset perturbation theory uses the difference between the Hartree–Fock Hamiltonian and the exact non-relativistic Hamiltonian as the perturbation. The zero-order energy is the sum of ...
6.1 Example of first-order perturbation theory – ground-state energy of the quartic oscillator 6.2 Example of first- and second-order perturbation theory – quantum pendulum 6.3 Potential energy as a perturbation
Rabi problem in time-dependent perturbation theory [ edit ] In the quantum approach, the periodic driving force can be considered as periodic perturbation and, therefore, the problem can be solved using time-dependent perturbation theory, with
The varying of the parameters drives the system. Examples of parameters that may be varied are its resonance frequency and damping . Parametric oscillators are used in many applications. The classical varactor parametric oscillator oscillates when the diode's capacitance is varied periodically. The circuit that varies the diode's capacitance is ...
The method removes secular terms—terms growing without bound—arising in the straightforward application of perturbation theory to weakly nonlinear problems with finite oscillatory solutions. [1] [2] The method is named after Henri Poincaré, [3] and Anders Lindstedt. [4]
Creation and annihilation operators can act on states of various types of particles. For example, in quantum chemistry and many-body theory the creation and annihilation operators often act on electron states. They can also refer specifically to the ladder operators for the quantum harmonic oscillator. In the latter case, the creation operator ...
Perturbation theory along with matching of solutions in domains of overlap and imposition of boundary conditions (different from those for the double-well) can again be used to obtain the eigenvalues of the Schrödinger equation for this potential. In this case, however, one expands around the central trough of the potential.