Related papers: Bound States by the Spinless Salpeter Equation
Motivated by the observation of a recent renewal of rather strong interest in the description of bound states by (semi-) relativistic equations of motion, we revisit, for the example of the Woods-Saxon interactions, the eigenvalue problem…
We review some important topics related to the semirelativistic description of bound states by the spinless Salpeter equation: the special case of the Coulomb interaction, numerical approximation methods, and a way to avoid the problematic…
Salpeter equations with potential functions rising to infinity in configuration space do not automatically predict stable bound states. For this to happen, also the Lorentz behaviour of the involved Bethe-Salpeter kernels is crucial. At…
We obtain, using the Birman-Schwinger method, upper limits on the total number of bound states and on the number of $\ell$-wave bound states of the semirelativistic spinless Salpeter equation. We also obtain a simple condition, in the…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…
The Bethe-Salpeter approach allows for quantum-field-theoretic descriptions of relativistic bound states; its inherent complexity, however, usually prevents to find its exact solutions. Under suitable simplifying assumptions about the…
Wheeler-DeWitt equation is applied to $k > 0$ Friedmann Robertson Walker metric with various types of matter. It is shown that if the Universe ends in the matter dominated era (e.g., radiation or pressureless gas) with zero cosmological…
In nonrelativistic limits for states labeled by minimum packets with constrained spatial spreads and over a short term, states of unconstrained quantum field theories evolve on trajectories described by Newton's equations for the $1/r^2$…
Besides perturbation theory, which requires, of course, the knowledge of the exact unperturbed solution, variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in…
The existence of bound states in quantum mechanics with no classical counterpart has been a subject of interest for a long time. Cross-wires and cavities connected to infinite leads are typical examples in which open geometries with bulges…
Besides perturbation theory (which clearly requires the knowledge of the exact unperturbed solution), variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in quantum…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
Several techniques for deriving semianalytical bounds on the energy eigenvalues of the spinless Salpeter equation and for estimating the quality of the corresponding approximate eigenstates are reviewed.
Relationships between the coupling constant and the binding energy of threshold bound states are obtained in a simple manner from an iterative algorithm for solving the eigenvalue problem. The absence of threshold bound states in higher…
We present a simple formula for finding bound state solution of any quantum wave equation which can be simplified to the form of $\Psi"(s)+\frac{(k_1-k_2s)}{s(1-k_3s)}\Psi'(s)+\frac{(As^2+Bs+C)}{s^2(1-k_3s)^2}\Psi(s)=0$. The two cases where…
Quantum wires and electromagnetic waveguides possess common features since their physics is described by the same wave equation. We exploit this analogy to investigate experimentally with microwave waveguides and theoretically with the help…
By introducing a boundary condition for the quantum wire, the Hubbard model is solved exactly by means of Bethe ansatz. The wave function for the bounded state is clearly defined, and the secular equation for the spectrum is exactly…
We establish a relation between the solution of a relativistic bound state equation in quantum mechanics and the field representation of a bound state with the aid of creation and annihilation operators. We show that a bound system can be…
The spinless Salpeter equation is the combination of relativistic kinematics with some static interaction potential. The nonlocal nature of the Hamiltonian resulting from this approximation renders difficult to obtain rigorous analytic…
We study the problem of the boundary conditions in the numerical simulation of closed and open quantum systems, described by a Schr\"odinger equation. On one hand, we show that a closed quantum system is defined by local boundary…