Quantum Mechanics
In the harmonic approximation the potential energy is a quadratic function of the normal coordinates. Solving the Schrödinger wave equation, the energy states for each normal coordinate are given by
- ,
where n is a quantum number that can take values of 0, 1, 2 ... The difference in energy when n changes by 1 are therefore equal to the energy derived using classical mechanics. See quantum harmonic oscillator for graphs of the first 5 wave functions. Knowing the wave functions, certain selection rules can be formulated. For example, for a harmonic oscillator transitions are allowed only when the quantum number n changes by one,
but this does not apply to an anharmonic oscillator; the observation of overtones is only possible because vibrations are anharmonic. Another consequence of anharmonicity is that transitions such as between states n=2 and n=1 have slightly less energy than transitions between the ground state and first excited state. Such a transition gives rise to a hot band.
Read more about this topic: Molecular Vibration
Famous quotes containing the words quantum and/or mechanics:
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (1896–1948)
“the moderate Aristotelian city
Of darning and the Eight-Fifteen, where Euclid’s geometry
And Newton’s mechanics would account for our experience,
And the kitchen table exists because I scrub it.”
—W.H. (Wystan Hugh)