Narrow Results

Using the Gazeau–Klauder and Klauder–Perelomov coherent states, we derive the Robertson–Schrödinger intelligent states for two-body Calogero quantum system.

This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system.¹ We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states à la Gazeau–Klauder and those à la Klauder–Perelomov, we derive the generalized intelligent states in analytical ways.

Intelligent states in the sense of field intensity dependent squeezing for a closed and symmetric algebra which interpolates between the Heisenberg Weyl algebra W₃ and su(1,1) algebra are constructed. The explicit expressions of these states in terms of Laguerre polynomials are derived and their quantum statistical properties are investigated.

We algebraically analyze the quantum Hall effect of a system of particles living on the disc B¹ in the presence of a uniform magnetic field B. For this, we identify the non-compact disc with the coset space SU(1,1)/U(1). This allows us to use the geometric quantization in order to get the wavefunctions as the Wigner -functions satisfying a suitable constraint. We show that the corresponding Hamiltonian coincides with the Maass Laplacian. Restricting to the lowest Landau level, we introduce the noncommutative geometry through the star product. Also we discuss the state density behavior as well as the excitation potential of the quantum Hall droplet. We show that the edge excitations are described by an effective Wess–Zumino–Witten action for a strong magnetic field and discuss their nature. We finally show that LLL wavefunctions are intelligent states.