This article discusses the rigid rotor in quantum mechanics. The kinetic energy of a rigid rotor is given in terms of the angular momentum. The angular momentum operator in spherical coordinates is derived.
Questions
- What is the kinetic energy of a rigid rotor?
- How is the angular momentum operator expressed in spherical coordinates?
- What is the difference between the classical and quantum mechanical descriptions of the rigid rotor?
Answers
- The kinetic energy of a rigid rotor is given by K = I * L^2 / 2, where I is the moment of inertia and L is the angular momentum.
- The angular momentum operator in spherical coordinates is given by Lx = -i*h * sin(theta) * d/dphi, Ly = -i*h * cos(theta) * d/dphi, and Lz = -i*h * (cot(theta) * sin(theta) * d/dtheta + cos(theta) * d/dphi).
- The classical and quantum mechanical descriptions of the rigid rotor differ in that the quantum mechanical description allows for discrete energy levels.