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:
“A personality is an indefinite quantum of traits which is subject to constant flux, change, and growth from the birth of the individual in the world to his death. A character, on the other hand, is a fixed and definite quantum of traits which, though it may be interpreted with slight differences from age to age and actor to actor, is nevertheless in its essentials forever fixed.”
—Hubert C. Heffner (1901–1985)
“It is only the impossible that is possible for God. He has given over the possible to the mechanics of matter and the autonomy of his creatures.”
—Simone Weil (1909–1943)