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The Morse potential, named after physicist Philip M. Morse, is a convenient interatomic interaction model for the potential energy of a diatomic molecule.It is a better approximation for the vibrational structure of the molecule than the quantum harmonic oscillator because it explicitly includes the effects of bond breaking, such as the existence of unbound states.
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.
This is a list of potential energy functions that are frequently used in quantum mechanics and have any meaning. ... (harmonic oscillator) Morse potential (morse ...
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.
The emission spectrum is more complicated than the absorption spectrum of the same molecule because there are more changes in vibrational energy level. The Morse potential (blue) and harmonic oscillator potential (green). The potential at infinite internuclear distance is the dissociation energy for pure vibrational spectra.
An oscillator is a physical system characterized by periodic motion, such as a pendulum, tuning fork, or vibrating diatomic molecule.Mathematically speaking, the essential feature of an oscillator is that for some coordinate x of the system, a force whose magnitude depends on x will push x away from extreme values and back toward some central value x 0, causing x to oscillate between extremes.
The potential-energy function of a harmonic oscillator is =. Given an arbitrary potential-energy function V ( x ) {\displaystyle V(x)} , one can do a Taylor expansion in terms of x {\displaystyle x} around an energy minimum ( x = x 0 {\displaystyle x=x_{0}} ) to model the behavior of small perturbations from equilibrium.
In the quantum mechanical picture, the vibrational levels and vibrational wavefunctions are those of quantum harmonic oscillators, or of more complex approximations to the potential energy of molecules, such as the Morse potential. Figure 1 illustrates the Franck–Condon principle for vibronic transitions in a molecule with Morse-like ...