相关论文: Quaternionic bound states
We describe the dynamics of a bound state of an attractive $\delta$-well under displacement of the potential. Exact analytical results are presented for the suddenly moved potential. Since this is a quantum system, only a fraction of the…
It is well known that (possibly non-unique) suitable field dynamics can be prescribed in spacetimes with timelike boundaries by means of appropriate boundary conditions. In Ref. [J. Math. Phys. {\bf 21}, 2802 (1980)], Wald derived a…
In this article, we answer the following question: If the wave equation possesses bound states but it is exactly solvable for only a single non-zero energy, can we find all bound state solutions (energy spectrum and associated…
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
Within the framework of fractional quantum mechanics, an exact solution has been found for the energy spectrum of a quantum particle confined in a quantum well - a symmetric one-dimensional finite potential well. A simple graphical…
In looking for quaternionic violations of quantum mechanics, we discuss the delay time for pure quaternionic potentials. The study shows in which energy region it is possible to amplify the difference between quaternionic and complex…
We determine approximate eigenvalues and eigenfunctions shapes for bound states in the $3D$ shallow spherical ultrarelativistic well. Existence thresholds for the ground state and first excited states are identified, both in the purely…
We use the tridiagonal representation approach to solve the radial Schr\"odinger equation for an inverse power-law potential of a combined quartic and sextic degrees and for all angular momenta. The amplitude of the quartic singularity is…
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…
Singularity of the potential function makes quantum tunneling problem mathematically underdetermined. To circumvent the difficulties it introduced in physics, a potential singularity cutoff is often used, followed by a reverse limit…
An explicit expression for the finite-volume energy shift of shallow three-body bound states for non-identical particles is obtained in the unitary limit. The inclusion of the higher partial waves is considered. To this end, the method of…
Quaternion quantum mechanics is examined at the level of unbroken SU(2) gauge symmetry. A general quaternionic phase expression is derived from formal properties of the quaternion algebra.
Transition states or quantum states of zero energy appear at the boundary between the discrete part of the spectrum of negative energies and the continuum part of positive energy states. As such, transition states can be regarded as a…
We present two novel solutions of real Hilbert state quaternionic quantum mechanics ($\mathbb H$QM). Firstly, we observe that the angular momentum operator admits two different classes of physically non-equivalent free particles. As a…
The spacings between bound-state levels of the Schr\"odinger equation with the same principal quantum number $N$ but orbital angular momenta $\ell$ differing by unity are found to be nearly equal for a wide range of power potentials $V =…
In quadrupole-bound anions, an extra electron is attached at a sufficiently large quadrupole moment of a neutral molecule, which is lacking a permanent dipole moment. The nature of the bound states and low-lying resonances of such anions is…
Dynamic equations concerning physical expectation values have been examined in terms of the real Hilbert space approach to quantum mechanics. The considered cases involve complex wave functions, as well as quaternionic wave functions. The…
The real Hilbert space formalism developed within the quaternionic quantum mechanics ($\mathbb H$QM) is fully applied to the simple model of the autonomous particle. This framework permits novel insights within the usual description of the…
We analyze the results obtained from a model consisting of the interaction etween the electric quadrupole moment of a moving particle and an electric field. We argue that the system does not support bound states because the motion along the…
We report a new class of hyperbolic asymmetric double-well whose bound state wavefunctions can be expressed in terms of confluent Heun functions. An analytic procedure is used to obtain the energy eigenvalues and the criterion for the…