Abstract
The Darboux transformation operator method is applied to the investigation of coherent states of transparent multisoliton potentials. An isometric correspondence between Hilbert spaces of the states of a free particle and a particle moving in the soliton potential is established. It is shown that the Darboux transformation operator being unbounded and closed cannot realize an isometric mapping between Hilbert spaces. A quasispectral representation of transformation operators in terms of continuous basis sets is obtained. Different families of coherent states of the multisoliton potential are introduced. Measures that realize the resolution of the unity in terms of the projectors on the coherent states vectors are calculated. These measures are defined by ordinary smooth functions for the states obtained with the help of bounded transformation operators and by generalized ones otherwise.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
