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Peer-reviewedCC BY 4.0Mathematics

Characteristic Function Operator

  • Leon Cohen1
  1. 1Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX 77840, USA
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Abstract

We define the characteristic function operator eiθA+iτB, where A and B are explicit functions of the operators x and D. Operators of this form arise in a wide range of applications, including quantum mechanics, evolution equations, and time–frequency analysis. We briefly review the historical development of the characteristic function operator and present a general method for evaluating its action on functions in both the spatial and Fourier domains. The method relies on solving the eigenvalue problem for θA+τB. A number of examples are presented. The method is then applied to the solution of evolution equations.

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Cite

BibTeXRIS
BibTeX
@article{cohen2026characteristic,
  title = {{Characteristic Function Operator}},
  author = {Leon Cohen},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203799},
  url = {https://www.mdpi.com/2227-7390/14/20/3799},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Characteristic Function Operator
AU  - Leon Cohen
PY  - 2026
DA  - 2026/10/19
JO  - Mathematics
DO  - 10.3390/math14203799
UR  - https://www.mdpi.com/2227-7390/14/20/3799
AB  - We define the characteristic function operator eiθA+iτB, where A and B are explicit functions of the operators x and D. Operators of this form arise in a wide range of applications, including quantum mechanics, evolution equations, and time–frequency analysis. We briefly review the historical development of the characteristic function operator and present a general method for evaluating its action on functions in both the spatial and Fourier domains. The method relies on solving the eigenvalue problem for θA+τB. A number of examples are presented. The method is then applied to the solution of evolution equations.
SN  - 2227-7390
ER  -