Related papers: Eigenfunctions for SU(N) particles with 1/r^2 inte…
We introduce to this paper new kinds of coherent states for some quantum solvable models: a free particle on a sphere, one-dimensional Calogero-Sutherland model, the motion of spinless electrons subjected to a perpendicular magnetic field…
Eigenstates in finite systems such as nuclei, atoms, atomic clusters and quantum dots with few excited particles are chaotic superpositions of shell model basis states. We study criterion for the equilibrium distribution of basis components…
We study the excitation energy spectrum in the S=1/2 ferromagnetic Ising spin chain with the easy axis z in a magnetic field h={h_x,0,h_z}. According to Wu and McCoy's scenario of weak confinement, the fermionic spinon excitations (kinks),…
Three exactly solvable Hamiltonians of complex structure are studied in the framework of a semi-classical approach. The quantized trajectories for intrinsic coordinates correspond to energies which may be classified in collective bands. For…
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined…
An integrable two-dimensional system related to certain fermion-soliton systems is studied. The self-consistent solutions of a static version of the system are obtained by using the tau function approach. The self-consistent solutions…
For a quantum system of N identical, harmonically interacting particles in a one-dimensional harmonic trap we calculate for the bosonic and fermionic ground state the corresponding 1-particle reduced density operator $\rho_1$ analytically.…
In this note we calculate the spectrum of two-dimensional QCD. We formulate the theory with SU(N_c) currents rather than with fermionic operators. We construct the Hamiltonian matrix in DLCQ formulation as a function of the harmonic…
We consider N fermions in a two-dimensional harmonic oscillator potential interacting with a very short-range repulsive pair-wise potential. The ground-state energy of this system is obtained by performing a Thomas-Fermi as well as a…
We present a study of the spectral properties like the energy spectrum, the eigenmodes and density of states of a classical finite system of two-dimensional (2D) charged particles which are confined by a quadratic potential. Using the…
We present an algebraic construction of the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement. These eigenfunctions are the superspace extension of the…
Analytic and approximate solutions for the energy eigenvalues generated by a confined softcore Coulomb potentials of the form a/(r+\beta) in d>1 dimensions are constructed. The confinement is effected by linear and harmonic-oscillator…
The 40-year-old Calogero-Sutherland (CS) model remains a source of inspirations for understanding 1d interacting fermions. At $\beta=1, \text{or}0$, the CS model describes a free non-relativistic fermion, or boson theory, while for generic…
We present essentially exact solutions of the Schroedinger equation for three fermions in two different spin states with zero-range s-wave interactions under harmonic confinement. Our approach covers spherically symmetric, strictly…
We study the localization of particles rotating in a two-dimensional harmonic potential by solving their rotational spectrum using many-particle quantum mechanics and comparing the result to that obtained with quantizing the rigid rotation…
There are few exactly solvable potentials in quantum mechanics for which the completeness relation of the energy eigenstates can be explicitly verified. In this article, we give an elementary proof that the set of bound (discrete) states…
We consider trial wavefunctions exhibiting SU(K) symmetry which may be well-suited to grasp the physics of the fractional quantum Hall effect with internal degrees of freedom. Systems of relevance may be either spin-unpolarized states…
Based on previous works, analytical calculational procedures for dealing with the strongly interacting fermions ground state are further developed through a medium dependent potential in terms of the Bethe-Peierls contact interaction model.…
We find for the first time the ground state energy and the optical absorption spectra for N electrons (holes) interacting with each other and with the longitudinal optical (LO) phonons at an arbitrary electron-phonon coupling strength…
We show that Jastrow-Slater wave functions, in which a density-density Jastrow factor is applied onto an uncorrelated fermionic state, may possess long-range order even when all symmetries are preserved in the wave function. This fact is…