相关论文: Quaternionic bound states
The effects of quantum confinement on the momentum distribution of electrons confined within a cylindrical potential well have been analyzed. The motivation is to understand specific features of the momentum distribution of electrons when…
Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class of new shape invariant potentials which are…
We analyze the results obtained from a model consisting of the interaction between a moving electric quadrupole moment and a magnetic field. We argue that there are no bound states contrary to what the author stated. It is shown that the…
We derive analytic expressions of the recursive solutions to the Schr\"{o}dinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately…
Bound state formation is a classic feature of quantum mechanics, where a particle localizes in the vicinity of an attractive potential. This is typically understood as the particle lowering its potential energy. In this article, we discuss…
A classic no-go theorem in one-dimensional quantum mechanics can be evaded when the potentials are unbounded below, thus allowing for novel parity-paired degenerate energy bound states. We numerically determine the spectrum of one such…
The quark-antiquark bound states are discussed using the relativistic spectator (Gross) equations. A relativistic covariant framework for analyzing confined bound states is developed. The relativistic linear potential developed in an…
We give precise meaning to piecewise constant potentials in non-commutative quantum mechanics. In particular we discuss the infinite and finite non-commutative spherical well in two dimensions. Using this, bound-states and scattering can be…
We find the minimum and the maximum value for the local energy of an arbitrary finite bipartite system for any given amount of entanglement, also identifying families of states reaching these bounds and sharing formal analogies with thermal…
We investigate the approximate bound state solutions of the Schr\"odinger equation for the PT-/non-PT-symmetric and non Hermitian Hellmann potential. Exact energy eigenvalues and corresponding normalized wave functions are obtained.…
The one-dimensional infinite square well is the simplest solution of quantum mechanics, and consequently one of the most important. In this article, we provide this solution using the real Hilbert space approach to quaternic quantum…
Quasi-normal modes (QNMs) of the massless scalar wave in $1+1$ dimensions are obtained for a symmetric, finite, triangular barrier potential. This problem is exactly solvable, with Airy functions involved in the solutions. Before obtaining…
Many-body quantum-mechanical stationary states that have real valued wavefunctions are shown to satisfy a classical conservation of energy equation with a kinetic energy function. The terms in the equation depend on the probability…
A quantum particle moving under the influence of singular interactions on embedded surfaces furnish an interesting example from the spectral point of view. In these problems, the possible occurrence of a bound state is perhaps the most…
We investigate a one-dimensional quantum system with a self-similar arrangement of delta-function potential barriers, exhibiting discrete scale invariance. The singular potential induces kinematically enforced symmetry breaking at $x=0$,…
A new approach to find exact solutions to one--dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known…
Basic theoretical issues relating to the response of confined relativistic particles are considered including the scaling of the response in spacelike and timelike regions of momentum transfer and the role of final state interactions. A…
In this work we investigate the quantum dynamics of an electric dipole in a $(2+1)$-dimensional conical spacetime. For specific conditions, the Schr\"odinger equation is solved and bound states are found with the energy spectrum and…
Others have solved the Schr\"odinger equation for a one-dimensional model having a square potential barrier in free-space by requiring an incident and a reflected wave in the semi-infinite pre-barrier region, two opposing waves in the…
After a review on recent results on quaternic quantum mechanics ($\mathbb{H}$QM), we present further consistency tests that reinforce its compatibility with the usual complex quantum mechanics ($\mathbb{C}$QM). The novel results comprises…