Abstract
We consider a class of phase space measures, which naturally arise in the Bohmian interpretation of quantum mechanics. We study the classical limit of these so-called Bohmian measures, in dependence on the scale of oscillations and concentrations of the sequence of wave functions under consideration. The obtained results are consequently compared to those derived via semi-classical Wigner measures. To this end, we shall also give a connection to the theory of Young measures and prove several new results on Wigner measures themselves. Our analysis gives new insight on oscillation and concentration effects in the semi-classical regime.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1542-1576 |
| Number of pages | 35 |
| Journal | Journal of Functional Analysis |
| Volume | 259 |
| Issue number | 6 |
| DOIs | |
| State | Published - Sep 2010 |
| Externally published | Yes |
Bibliographical note
Funding Information:✩ This publication is based on work supported by Award No. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology (KAUST). Christof Sparber has been supported by the Royal Society via his University research fellowship and Peter Markowich by his Royal Society Wolfson Research Merit Award. * Corresponding author. E-mail addresses: [email protected] (P. Markowich), [email protected] (T. Paul), [email protected] (C. Sparber).
Keywords
- Bohmian mechanics
- Classical limit
- Quantum mechanics
- Weak convergence
- Wigner function
- Young measures
ASJC Scopus subject areas
- Analysis