04082010supplemental

04082010supplemental - Quantum Mechanics Vibration and...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Quantum Mechanics: Vibration and Rotation of Molecules 5th April 2010 I. Classical Orbital Angular Momentum and Extension to Q. M. Operators Before considering the eigenvalue equations describing the energetics and eigenfunctions for describing orbital angular momentum in a q.m. sense, we will first consider the operators that are pertinent to measurements of angular momentum on such systems (remembering that operators are asso- ciated with measureables/observables in a q.m. sense). We also note that we will consider angular momentum in general, though the formulation in the following is based on classical analogues, which are based on analogy to orbital motion). We have considered, so far, the translational (particle-in-a- box) and vibrational (harmonic-oscillator) models to describe translational and vibrational dynamical modes as we understand in classical mechanics. With a discussion of angular momentum, we focus on the rotational model of such dynamics to arrive at a complete set of eigenfunctions that we can apply towards describing actual systems, such as atoms and molecules. Consider a particle described by the Cartesian coordinates ( x, y, z ) ≡ r and their conjugate momenta ( p x , p y , p z ) ≡ p The classical definition of the orbital angular momentum of such a par- ticle about the origin is L = r × p giving, L x = y p z- z p y , (1) L y = z p x-...
View Full Document

This note was uploaded on 02/02/2012 for the course CHEM 444 taught by Professor Dybowski,c during the Fall '08 term at University of Delaware.

Page1 / 4

04082010supplemental - Quantum Mechanics Vibration and...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online