Presentation on theme: "Classical Model of Rigid Rotor"— Presentation transcript:
1 Classical Model of Rigid Rotor A particle rotating around a fixed point, as shown below, has angular momentum and rotational kinetic energy (“rigid rotor”)The classical kinetic energy is given by:If the particle is rotating about a fixed point at radius r with a frequency ʋ (s−1 or Hz), the velocity of the particle is given by:where ω is the angular frequency (rad s−1 or rad Hz). The rotational kinetic energy can be now expressed as:Alsowhere
2 Note that there is no potential energy involved in free rotation. Consider a classical rigid rotor corresponding to a diatomic molecule. Here we consider only rotation restricted to a 2-D plane where the two masses (i.e., the nuclei) rotate about their center of mass.The rotational kinetic energy for diatomic molecule in terms of angular momentumNote that there is no potential energy involved in free rotation.
3 Momentum Summary Classical QM Linear Momentum Energy Rotational (Angular)MomentumEnergy
18 Rigid Rotor in Quantum Mechanics Transition from the above classical expression to quantum mechanics can be carried out by replacing the total angular momentum by the corresponding operator:Wave functions must contain both θ and Φ dependence:are called spherical harmonics