Related papers: Accuracy of Semiclassical Methods for Shape Invari…
We present a comprehensive study of the quasinormal modes of a new class of nonlocal static and spherically symmetric black hole (BH) solutions within the framework of the revised Deser-Woodard theory of gravity. These solutions are…
This is an unconventional review article on spectral problems in black hole perturbation theory. Our purpose is to explain how to apply various known techniques in quantum mechanics to such spectral problems. The article includes…
Quantum mechanical WKB-method is elaborated for the known quantum Kepler problem in curved 3-space models Euclide, Riemann and Lobachevsky in the framework of the complex variable function theory. Generalized Schr\"{o}dinger, Klein-Fock…
The analytical transfer matrix technique is applied to the Schr\"{o}dinger equation of symmetric quartic-well potential problem in the form $V(x)={1/2}kx^{2}+\lambda{x^{4}}.$ This gives quantization condition from which we can calculate the…
We present a semiclassical treatment of one-dimensional many-body quantum systems in equilibrium, where quantum corrections to the classical field approximation are systematically included by a renormalization of the classical field…
A regular form of the Schwarzschild geometry is proposed. It is more suitable for application in microphysics because the source mass comes out both as a Schwarzschild radius and the Compton wavelength of the mass $m$. The Komar energy…
We present a nonparametric method to determine the sign of $w+1$ in the equation of state of dark energy. It is based on geometrical behaviour and is more tolerant to uncertainties of other cosmological parameters than fitting methods. It…
We explore the possibility of modifying the Lewis-Riesenfeld method of invariants developed originally to find exact solutions for time-dependent quantum mechanical systems for the situation in which an exact invariant can be constructed,…
For a quantum mechanical system with broken supersymmetry, we present a simple method of determining the ground state when the corresponding energy eigenvalue is sufficiently small. A concise formula is derived for the approximate ground…
We obtain analytical solutions of the two-body spinless Salpeter (SS) equation with Yukawa potential within the conventional approximation scheme to the centrifugal term for any -state. The semi-relativistic bound state energy spectra and…
We develop semiclassical approximations for calculating photoabsorption cross sections beyond the continuum threshold in quantum many-body systems. These approximations use the fully quantum-mechanical Wigner function of the ground state…
Quantum deformed potentials arise naturally in quantum mechanical systems of one bosonic coordinate coupled to $N_f$ Grassmann valued fermionic coordinates, or to a topological Wess-Zumino term. These systems decompose into sectors with a…
A detailed comparison of the expressions for the decay widths obtained within the semiclassical WKB approximation using different approaches to the tunneling problem is performed. The differences between the available improved formulae for…
Accurate simulations of molecules require high-level electronic-structure theory in combination with rigorous methods for approximating the quantum dynamics. Machine-learning approaches can significantly reduce the computational expense of…
We apply the canonical perturbation theory to the semi--quantal hamiltonian of the SU(3) shell model. Then, we use the Einstein--Brillowin--Keller quantization rule to obtain an analytical semi--quantal formula for the energy levels, which…
Using a new analytic quantum mechanical method based on Slater's Xalpha method, we show that a fairly accurate estimate of the total energy of a molecule can be obtained from the exact energies of its constituent atoms. The mean absolute…
We study the quantum-mechanical bootstrap as it applies to the bound states of several central potentials in three dimensions. As part of this effort, we show how the bootstrap approach may be applied to ``non-algebraic'' potentials, such…
Exploring gravitational theories beyond general relativity (GR) with black hole (BH) spectroscopy requires accurate and flexible methods for computing their quasinormal mode (QNM) spectrum. A popular method of choice is the higher-order…
Using the method of the "exact discretization" of the Schr\"odinger equation, we propose a particular discretized version of the N=2 Supersymmetric Quantum Mechanics. After defining the corresponding shape invariance condition, we show that…
The WKB approximation for deformed space with minimal length is considered. The Bohr-Sommerfeld quantization rule is obtained. A new interesting feature in presence of deformation is that the WKB approximation is valid for intermediate…