Deformed Harmonic Oscillator Algebras defined by their Bargmann representations

Details Deformed Harmonic Oscillator Algebras defined by their Bargmann representations Deformed Harmonic Oscillator Algebras defined by their Bargmann representations

1997-12-17

arxiv.org/abs/q-alg/9712043v1

Mathematics

Quantum Algebra

27 pages, Latex

Scientific paper

Deformed Harmonic Oscillator Algebras are generated by four operators, two mutually adjoint $a$ and $a^\dagger$, and two self-adjoint $N$ and the unity $1$ such as: $[a,N] = a, [a^\dagger, N]= -a^\dagger, a^\dagger a = \psi(N)$ and $aa^\dagger =\psi(N+1)$. The Bargmann Hilbert space is defined as a space of functions, holomorphic in a ring of the complex plane, equipped with a scalar product involving a true integral. In a Bargmann representation, the operators of a Deformed Harmonic Oscillator Algebra act on a Bargmann Hilbert space and the creation (or the annihilation operator) is the multiplication by $z$. We discuss the conditions of existence of Deformed Harmonic Oscillator Algebras assumed to admit a given Bargmann representation.

Affiliated with

Also associated with

No associations

Rating

Deformed Harmonic Oscillator Algebras defined by their Bargmann representations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Deformed Harmonic Oscillator Algebras defined by their Bargmann representations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deformed Harmonic Oscillator Algebras defined by their Bargmann representations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-677738