# Temperature-Dependent Rotational Energy Spectrum

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This Demonstration studies the pure rotational spectrum of the quantum rigid rotor problem (neglecting centrifugal distortion), described by the Hamiltonian , where is the angular momentum operator and is the moment of inertia. The energy levels are given by , where is the rotational constant and the transition frequency between two adjacent levels is (selection rules only allow transitions that satisfy ). The left graphic shows the spectrum consisting of a series of equally spaced lines, where the relative intensity of each line depends on the probability to occupy the initial state in thermal equilibrium, , where is the Boltzmann constant and is the temperature. The left and right graphics show the spectrum for a given ratio and the energy level diagram, and the red highlighting shows the correspondence between a pair of energy levels and a specific transition frequency.

Contributed by: Porscha McRobbie and Eitan Geva (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

detailSectionParagraph## Permanent Citation

"Temperature-Dependent Rotational Energy Spectrum"

http://demonstrations.wolfram.com/TemperatureDependentRotationalEnergySpectrum/

Wolfram Demonstrations Project

Published: March 7 2011