On Quantum Integrable Systems

Technical Report · Tue Nov 01 00:00:00 EDT 2011

DOI:https://doi.org/10.2172/1036292· OSTI ID:1036292

Danilov, Viatcheslav; Nagaitsev, Sergei

Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and nonlinear integrable plasma traps. Now, all classical results are carried over to a nonrelativistic quantum case. In this paper we have described an extension of the Ermakov-like transformation to the Schroedinger and Pauli equations. It is shown that these newly found transformations create a vast variety of time dependent quantum equations that can be solved in analytic functions, or, at least, can be reduced to time-independent ones.

• Research Organization: Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: AC02-07CH11359
• OSTI ID: 1036292
• Report Number(s): FERMILAB-FN-0938-AD; arXiv eprint number arXiv:1111.4264; TRN: US1201386
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCELERATORS
ANALYTIC FUNCTIONS
PHYSICS
PLASMA
TRANSFORMATIONS
General Physics