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We present a phase-space electronic Hamiltonian ĤPS (parameterized by both nuclear position X and momentum P) that boosts each electron into the moving frame of the nuclei that are closest in real space. The final form for the phase space Hamiltonian does not assume the existence of an atomic orbital basis, and relative to standard Born–Oppenheimer theory, the newly proposed one-electron operators can be expressed directly as functions of electronic and nuclear positions and momentum. We show that (i) quantum–classical dynamics along such a Hamiltonian maintains momentum conservation and that (ii) diagonalizing such a Hamiltonian can recover the electronic momentum and electronic current density reasonably well. In conjunction with other reports in the literature that such a phase-space approach can also recover vibrational circular dichroism spectra, we submit that the present phase-space approach offers a testable and powerful approach to post-BO electronic structure theory. Moreover, the approach is inexpensive and can be immediately applied to simulations of chiral induced spin selectivity experiments (where the transfer of angular momentum between nuclei and electrons is considered critical).
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How to measure the momentum of single quanta
The von Neumann theory of measurement, based on an ultimate entanglement of the quantum observable with a classical machine followed by decoherence or collapse, does not readily apply to most measurements of momentum. Indeed, how we measure the momentum of a quantum particle is not even discussed in most quantum mechanics textbooks. Instead, we often teach the lore that position, and momentum cannot be measured at the same time. Yet, most ways to measure momentum actually involve measuring position to infer momentum. In this tutorial review, I examine real experiments that measure momentum and describe how one can improve our teaching of the theory of measurement when we focus on real experiments, rather than abstract mathematical models of measurement.
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- Award ID(s):
- 1915130
- PAR ID:
- 10552551
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- The European Physical Journal Special Topics
- Volume:
- 232
- Issue:
- 20-22
- ISSN:
- 1951-6355
- Page Range / eLocation ID:
- 3285 to 3294
- Subject(s) / Keyword(s):
- quantum measurement momentum
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1140/epjs/s11734-023-00967-6
