Related papers: Quaternionic bound states
By using the recent mathematical tools developed in quaternionic differential operator theory, we solve the Schroedinger equation in presence of a quaternionic step potential. The analytic solution for the stationary states allows to…
Quantum mechanics in a one--parameter family of volcano potentials is investigated. After a discussion on their construction and classical mechanics, we obtain exact, normalisable bound states for specific values of the energy. The nature…
The Schrodinger equation for a particle moving in a square well potential with BenDaniel - Duke boundary conditions is solved. Using algebraic approximations for trigonometric functions, the transcendental equations of the bound states…
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…
We revisit the problem of quantum tunneling for a particle moving in the continuum, and in the absence of a magnetic field. In all spatial dimensions, we extend previous results to the case where the single-well potential satisfies…
In this work we show the quaternionic quantum descriptions of physical processes from the Planck to macro scale. The results presented here are based on the concepts of the Cauchy continuum and the elementary cell at the Planck scale. The…
A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form…
The procedure commonly used in textbooks for determining the eigenvalues and eigenstates for a particle in an attractive Coulomb potential is not symmetric in the way the boundary conditions at $r=0$ and $r \rightarrow \infty$ are…
A square potential well with position-dependent mass is studied for bound states. Applying appropriate matching conditions, a transcendental equation is derived for the energy eigenvalues. Numerical results are presented graphically and the…
One of the most widely problem studied in quantum mechanics is of an infinite square-well potential. In a minimal-length scenario its study requires additional care because the boundary conditions at the walls of the well are not well…
We propose a simple and straightforward method based on Wronskians for the calculation of bound--state energies and wavefunctions of one--dimensional quantum--mechanical problems. We explicitly discuss the asymptotic behavior of the…
We summarize unusual bound or localized states in quantum mechanics. Our guide through these intriguing phenomena is the classical physics of the upside-down pendulum. Taking advantage of the analogy between the corresponding Newton's…
We discuss the arising of bound states solutions of the Schr\"odinger equation due to the presence of a Coulomb-type potential induced by the interaction between a moving electric quadrupole moment and a magnetic field. Furthermore, we…
We propose a new class of fundamental solutions for the numerical analysis of boundary value problems for the Maxwell equations. We prove completeness of systems of such fundamental solutions in appropriate Sobolev spaces on a smooth…
In modern fundamental theories there is consideration of higher dimensions, often in the context of what can be written as a Schr\"odinger equation. Thus, the energetics of bound states in different dimensions is of interest. By considering…
We construct solitary wave solutions in a $1+1$ dimensional massless scalar ($\phi$) field theory with a specially chosen potential $V(\phi)$. The equation governing perturbations about this solitary wave has an effective potential which is…
We study the problem of the attractive inverse square potential in quantum mechanics with a generalized uncertainty relation. Using the momentum representation, we show that this potential is regular in this framework. We solve analytically…
We present a method enabling us to write in relativistic manner the wave function of some particular two particle bound state models in quantum mechanics. The idea is to expand the bound state wave function in terms of free states and to…
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear…
Quantum particles interacting with potential barriers are ubiquitous in physics, and the question of how much time they spend inside classically forbidden regions has attracted interest for many decades. Recent developments of new…