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A possible candidate for the present accelerated expansion of the Universe is ''phantom energy'', which possesses an equation of state of the form $\omega\equiv p/\rho<-1$, consequently violating the null energy condition. As this is the…
A new idea of the cosmological constant is proposed in this paper. Due to the horizon is limited, the quantum fluctuation of the inflaton field is not zero, a nonzero vacuum energy is remained as a residual inflationary energy of an unusual…
Single particle scattering around zero energy is re-analysed in view of recent experiments with ultra-cold atoms, nano-structures and nuclei far from the stability valley. For non-zero orbital angular momentum the low energy scattering…
Usually, the reflection probability $R(E)$ of a particle of zero energy incident on a potential which converges to zero asymptotically is found to be 1: $R(0)=1$. But earlier, a paradoxical phenomenon of zero reflection at zero energy…
The motion in a simple, time independent rational galactic potential is studied. The potential is a generalization of a two dimensional harmonic oscillator potential and can be considered to describe plane motion in the central parts of a…
We improve upon the simple model studied by Casadio and Orlandi [JHEP 1308 (2013) 025] for a black hole as a condensate of gravitons. Instead of the harmonic oscillator potential, the P\"oschl-Teller potential is used, which allows for a…
A concept of kinetic energy in quantum mechanics is analyzed. Kinetic energy is a non-zero positive value in many cases of bound states, when a wave function is a real-valued one and there are no visible motion and flux. This can be…
We study a one-dimensional singular potential plus three types of regular interactions: constant electric field, harmonic oscillator and infinite square well. We use the Lippman-Schwinger Green function technique in order to search for the…
Canyon landscapes in high dimension can be described as manifolds of small, but extensive dimension, immersed in a higher dimensional ambient space and characterized by a zero potential energy on the manifold. Here we consider the problem…
The newly developed single trajectory quadrature method is applied to solve the ground state quantum wave function for Coulomb plus linear potential. The general analytic expressions of the energy and wave function for the ground state are…
We perform a study of various anharmonic potentials using a recently developed method. We calculate both the wave functions and the energy eigenvalues for the ground and first excited states of the quartic, sextic and octic potentials with…
The total energy of the ground state of the quantum harmonic oscillator is obtained with minimal assumptions. The vacuum energy density of the universe is derived and a cutoff frequency is obtained for the upper bound of the quantum…
We explore a collapsing cosmology driven by a scalar field which is minimally coupled to gravity in a spatially at and spherically symmetric, isotropic and homogeneous space-time, with a variable timescale that avoids the final singularity.…
The thermodynamic properties of black holes -- temperature, entropy and radiation rates -- are usually associated with the presence of a horizon. We argue that any Extremely Compact Object (ECO) must have the {\it same} thermodynamic…
We present a quantum harmonic oscillator model of a collapsed star trapped in the potential well of its gravitational field. The model incorporates quantum matter (quantum fields) as a source to classical gravitational field. We describe…
We consider two situations that can be modeled by oscillators. First we show that the universe itself is a normal mode of Planck scale oscillators. Next we show that a background Zero Point Field or dark energy can be modeled by…
The quantum properties of solitons at one loop can be related to phase shifts of waves on the soliton background. These can be combined with heat kernel methods to calculate various parameters. The vacuum energy of a CP(1) soliton in 2+1…
In this lecture we outline the main results of our investigations of certain field-theoretic systems which have V-shaped field potential. After presenting physical examples of such systems, we show that in static problems the exact ground…
A new exact analytically solvable Eckart-type potential is presented, a generalisation of the Hulthen potential. The study through Supersymmetric Quantum Mechanics is presented together with the hierarchy of Hamiltonians and the shape…
An infinite sequence of potential well functions is considered. A numerical method is used for the Schr$\ddot{\text{o}}$dinger equation to obtain the energy eigenvalue spectra for a number of these potential well functions. The results for…