Quantum dynamics of a semi-infinite homogeneous harmonic chain

✍ Scribed by Domingo Prato; Pedro W. Lamberti

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 464 KB
• Volume: 197
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(93)90470-o

✦ Synopsis

The quantum dynamics of a semi-infinite homogeneous harmonic chain is studied. Assuming the system to be in its ground state, a harmonic motion, A sin(or), is imposed on the mass at the beginning of the chain. The quantum state of the system for t > 0 is calculated by means of the evolution operator.

Two different regimes occur: one for angular frequencies o outside the allowed band o > or),, and the other one for o inside the band. After a transient the time derivative of the total energy of the chain vanishes for the first regime and tends to a constant for the second one. The mean values of the displacements from their equilibrium position are also calculated for masses along the chain. These averaged displacements and the time derivative of the total energy are shown to give exactly the same expression as in the classical case.