Related papers: Relativistic N-Boson Systems Bound by Oscillator P…
We study the lowest energy E of a relativistic system of N identical bosons bound by pair potentials of the form V(r_{ij}) = g(r_{ij}^2) in three spatial dimensions. In natural units hbar = c = 1 the system has the semirelativistic…
We study the lowest energy E of a semirelativistic system of N identical massless bosons with Hamiltonian H= sum{i=1 to N} sqrt(p_i^2)+ sum{j>i=1 to N} g |r_i - r_j|^2, g > 0. We prove the inequalities A [g N^2 (N-1)^2]^{1/3} < E < B [g N^2…
General analytic energy bounds are derived for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N \sqrt(p_i^2+m^2) + \sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. A…
We establish bounds on the energy of a system of N identical bosons bound by attractive pair potentials and obeying the semirelativistic Salpeter equation. The lower bound is provided by a `reduction', with the aid of Jacobi relative…
We study the eigenvalues E_{n\ell} of the Salpeter Hamiltonian H = \beta\sqrt(m^2 + p^2) + vr^2, v>0, \beta > 0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided, the simple…
General analytic energy bounds are derived for N-boson systems governed by ultrarelativistic Hamiltonians of the form H = sum_{i=1}^N||p_i|| + sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. It is proved that a…
Analytic energy bounds for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N(p_i^2 + m^2)^{1/2} - sum_{1=i<j}^N v/r_{ij}, with v>0, are derived by use of Jacobi relative coordinates. For gravity v=c/N,…
We study a bound system of N identical bosons interacting by model pair potentials of the form V(r) = A sgn(p)r^p + B/r^2, A > 0, B >= 0. By using a variational trial function and the `equivalent 2-body method', we find explicit upper and…
Consider an N-Boson system interacting via a two-body repulsive short-range potential $V$ in a three dimensional box $\Lambda$ of side length $L$. We take the limit $N, L \to \infty$ while keeping the density $\rho = N / L^3$ fixed and…
The semirelativistic Hamiltonian H = \beta\sqrt{m^2 + p^2} + V(r), where V(r) is a central potential in R^3, is concave in p^2 and convex in p. This fact enables us to obtain complementary energy bounds for the discrete spectrum of H. By…
We study the spectrum of the spinless-Salpeter Hamiltonian H = \beta \sqrt{m^2 + p^2} + V(r), where V(r) is an attractive central potential in three dimensions. If V(r) is a convex transformation of the Coulomb potential -1/r and a concave…
The spinless Salpeter equation may be considered either as a standard approximation to the Bethe--Salpeter formalism, designed for the description of bound states within a relativistic quantum field theory, or as the most simple, to a…
A nonpolynomial one-dimensional quantum potential in the form of an isotonic oscillator (harmonic oscillator with a centripetal barrier) is studied. We provide the non-relativistic bound state energy spectrum E_{n} and the wave functions…
For systems of $N$ charged fermions (e.g. electrons) interacting with longitudinal optical quantized lattice vibrations of a polar crystal we derive upper and lower bounds on the minimal energy within the model of H. Fr\"ohlich. The only…
In this work we investigate small clusters of bosons using the hyperspherical harmonic basis. We consider systems with $A=2,3,4,5,6$ particles interacting through a soft inter-particle potential. In order to make contact with a real system,…
The lower bound masses of the ground-state relativistic three-boson system in 1+1, 2+1 and 3+1 space-time dimensions are obtained. We have considered a reduction of the ladder Bethe-Salpeter equation to the light-front in a model with…
The well known relation of Einstein relativistic energy for a free particle is extended to cover the total relativistic energy of a bound particle by calculating the relativistic potential energy. A non dissipative harmonic oscillator…
In the Nelson model particles interact through a scalar massless field. For hydrogen-like atoms there is a nucleus of infinite mass and charge $Ze$, $Z > 0$, fixed at the origin and an electron of mass $m$ and charge $e$. This system forms…
Consider $N$ bosons in a finite box $\Lambda= [0,L]^3\subset \mathbf R^3$ interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives the following upper bound on the ground state energy…
The quantum $N$-body problem is studied in the context of nonrelativistic quantum mechanics with a one-dimensional deformed Heisenberg algebra of the form $[\hat x,\hat p]=i(1+\beta \hat p^2)$, leading to the existence of a minimal…