H-Theorem in an Isolated Quantum Harmonic Oscillator

Che Hsiu Hsueh, Chi Ho Cheng, Tzyy Leng Horng, Wen Chin Wu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider the H-theorem in an isolated quantum harmonic oscillator through the time-dependent Schrödinger equation. The effect of potential in producing entropy is investigated in detail, and we found that including a barrier potential into a harmonic trap would lead to the thermalization of the system, while a harmonic trap alone would not thermalize the system. During thermalization, Shannon entropy increases, which shows that a microscopic quantum system still obeys the macroscopic thermodynamics law. Meanwhile, initial coherent mechanical energy transforms to incoherent thermal energy during thermalization, which exhibiting the decoherence of an oscillating wave packet featured by a large decreasing of autocorrelation length. When reaching thermal equilibrium, the wave packet comes to a halt, with the density distributions both in position and momentum spaces well-fitted by a microcanonical ensemble of statistical mechanics.

Original languageEnglish
Article number1163
Issue number8
Publication statusPublished - 2022 Aug


  • barrier potential
  • decoherence
  • H-theorem
  • quantum harmonic oscillator
  • Shannon entropy
  • thermalization

ASJC Scopus subject areas

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • Electrical and Electronic Engineering


Dive into the research topics of 'H-Theorem in an Isolated Quantum Harmonic Oscillator'. Together they form a unique fingerprint.

Cite this