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Starting from relativistic mass-less Madelung fluid, we shall develop a class of typical wave functions by imposing it to maximize Shannon entropy given its finite average quantum potential. We show that there is a class of solutions in…
The classical equations of motion of a charged particle in a spherically symmetric distribution of magnetic monopoles can be transformed into a system of linear equations, thereby providing a type of integrability. In the case of a single…
We make two observations on the motion of coupled particles in a periodic potential. Coupled pendula, or the space-discretized sine-Gordon equation is an example of this problem. Linearized spectrum of the synchronous motion turns out to…
The "particle in a box" problem is investigated for a relativistic particle obeying the Klein-Gordon equation. To find the bound states, the standard methods known from elementary non-relativistic quantum mechanics can only be employed for…
We consider eigenfunctions of a semiclassical Schr{\"o}dinger operator on an interval, with a single-well type potential and Dirichlet boundary conditions. We give upper/lower bounds on the L^2 density of the eigenfunctions that are uniform…
One dimensional quantum mechanics problems, namely the infinite potential well, the harmonic oscillator, the free particle, the Dirac delta potential, the finite well and the finite barrier are generalized for finite arbitrary dimension in…
We show that from an appropriate manipulation of the biconfluent Heun differential equation can obtain the correct expression for the energy eigenvalues for the Klein-Gordon equation without potential in the background of Som-Raychaudhuri…
Theoretically, in (1+1) dimensions, one can have Klein-Fock-Gordon-Majorana (KFGM) particles. More precisely, these are one-dimensional (1D) Klein-Fock-Gordon (KFG) and Majorana particles at the same time. In principle, the wave equations…
We prove essential self-adjointness of the spatial part of the linear Klein-Gordon operator with external potential for a large class of globally hyperbolic manifolds. The proof is conducted by a fusion of new results concerning globally…
We show that, given any static spacetime whose spatial slices are asymptotically Euclidean (or, more generally, asymptotically conic) manifolds modeled on the large end of the Schwarzschild exterior, there exist stationary solutions to the…
We examine the deformation quantization of a single particle moving in one dimension (i) in the presence of an infinite potential wall, (ii) confined by an infinite square well, and (iii) bound by a delta function potential energy. In…
We consider a U(1)-invariant nonlinear Klein-Gordon equation in dimension one or larger, self-interacting via the mean field mechanism. We analyze the long-time asymptotics of finite energy solutions and prove that, under certain generic…
Recently, scattering of a Klein-Gordon particle in the presence of mixed scalar-vector generalized symmetric Woods-Saxon potential was investigated for the spin symmetric and the pseudo-spin symmetric limits in one spatial dimension. In…
Recently, it has been investigated how the thermodynamic functions vary when the surface interactions are taken into account for a nucleon which is confined in a Woods-Saxon potential well, with a non-relativistic point of view. In this…
Using the pseudo-invariant operator method, we investigate the model of a particle with a time-dependent mass in a complex time-dependent symmetric potential well $V\left( x,t\right) =if\left(t\right) \left\vert x\right\vert$. The problem…
The particle in a well in dimension one is a classical problem in quantum mechanics. We study higher-dimensional analogues of the problem, where the well is a smooth domain in $\mathbb{R}^d$. We show that simple eigenvalues and…
The existence of a minimal length is predicted by theories of quantum gravity and it is generally accepted that this minimal length should be of the order of the Planck length and hence can be observed in high energy phenomenon. We study…
Explicit path integration is carried out for the Green's functions of special relativistic harmonic oscillators in (1+1)- and (3+1)-dimensional Minkowski space-time modeled by a Klein-Gordon particle in the universal covering space-time of…
The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection $A$ on a line bundle $L$ and a section $\phi$ of another…
We consider scalar and spinor particles in the spacetime of a domain wall in the context of low energy effective string theories, such as the generalized scalar-tensor gravity theories. This class of theories allows for an arbitrary…