Single-particle spectrum

{{Short description|Continuum of a physical particle-based quantity}}

{{refimprove |date=June 2025}}

The single-particle spectrum is a distribution of a physical quantity such as energy or momentum.

In formal Quantum field theory, a single-particle spectrum is defined as: "the spectrum of the operators of H, P on the space B."{{cite book|url=https://books.google.com/books?id=QNPkDwAAQBAJ&pg=PT316&dq=%22Single-particle+spectrum%22+-wikipedia&hl=en&newbks=1&newbks_redir=0&source=|title=Mathematical Foundations of Quantum Field Theory|first=Albert |last=Schwarz |year=2020|accessdate=June 4, 2025}}

The study of particle spectra allows us to visualize the global picture of particle production.{{cite book|url=https://books.google.com/books?id=NihGIUfKF24C&q=%22Single-particle+spectrum%22+-wikipedia&dq=%22Single-particle+spectrum%22+-wikipedia&hl=en&newbks=1&newbks_redir=0&source=|pages=18-19|title=Single Particle Mass Spectrometry Combustion Source Characterization and Atmospheric Apportionment of Vehicular, Coal and Biofuel Exhaust Emissions|first=David Townsend |last=Suess|publisher=The University of California at Riverside |year=2002|accessdate=June 4, 2025}} This is especially helpful for visualizing the structure of nanoparticles.{{cite journal|url=https://www.nature.com/articles/s41467-018-06397-6|title=Single Particle Automated Raman Trapping Analysis|first1=Jelle |last1=Penders|first2=Isaac J. |last2=Pence|journal=Nature Communications|volume=9|number=4256 |year=2018|accessdate=June 4, 2025}}

The existence of a "non-smooth" single-particle spectrum is a piece of evidence (proof) that the Fermi level exists.{{cite book|url=https://books.google.com/books?id=CrYyEQAAQBAJ&pg=PA240&dq=%22Single-particle+spectrum%22+-wikipedia&hl=en&newbks=1&newbks_redir=0&source=|page=240|title=Introductory Nuclear Physics|first=Samuel S. M. |last=Wong |isbn=9783527414451|publisher=Wiley|year=2024|accessdate=June 4, 2025}}

The spectrum are particles that are in space: "the single particle spectrum overlaps ... and the excitations of the electron gas becomes a particle."{{cite book|url=https://books.google.com/books?id=xJQ3BQAAQBAJ&pg=PA85&dq=%22Single-particle+spectrum%22+-wikipedia&hl=en&newbks=1&newbks_redir=0&source=|page=85|title=Festkorper Probleme: Advances in Solid State Physics, Volume 9|first=O. |last=Madelung|year=1969|publisher=Elsevier Science |accessdate=June 4, 2025}} This process uses Raman spectroscopy, developed by Chandrasekhar Venkata Raman.