# Temperature-Dependent Rotational Energy Spectrum

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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