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##

2.1.2 Quantum Oscillators

Application of quantum mechanics to the diatomic system leads to several
important conclusions:

- The system cannot be observed at any random vibrational energy between
and as depicted in Section 2.1.1.
- The vibrational energy of a given state is related to the classical
frequency of oscillation.

where *v* is the vibrational quantum number, *h* is Planck's
constant and is the classical frequency of oscillation. In
other words, the possible energies for a system are discrete, as given
by states described by the vibrational quantum number *v*.
- The energy
*between* two discrete states is also discrete. The
energy required to change states corresponds to the discrete energy
between states.
- The vibrational state can be changed by absorption (or emission) of
infrared light, provided:

- The light frequency is equal to the frequency of the equivalent classical
oscillator.
- The transition between the states is allowed (See Section2.1.4).

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** Up:** 2.1 General Theory of
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John S. Riley, DSB Scientific Consulting