Related papers: Bohr-Sommerfeld quantization and meson spectroscop…
We study the quantum propagator in the semiclassical limit with sharp confining potentials. Including the energy-dependent scattering phase due to sharp confining potential, the modified Van Vleck's formula is derived. We also discuss the…
Baryons containing two heavy quarks are treated in the Born-Oppenheimer approximation. Schr\"odinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter…
A certain modification of the semiclassical quantization condition based on the summarization of the known power expansion in the squared Planck constant is proposed. Corresponding deviation from exact spectra arises only together with the…
A relativistic two-body wave equation, local in configuration space, is derived from the Bethe-Salpeter equation for two scalar particles bound by a scalar Coulomb interaction. The two-body bound-state wave equation is solved analytically,…
Wave equations with energy-dependent potentials appear in many areas of physics, ranging from nuclear physics to black hole perturbation theory. In this work, we use the semi-classical WKB method to first revisit the computation of bound…
An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to $N\pi$, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the…
Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two and three dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurations are considered, one in which a…
In this paper we describe the spectrum of the quantum periodic Benjamin-Ono equation in terms of the multi-phase solutions of the underlying classical system (the periodic multi-solitons). To do so, we show that the semi-classical…
Quantum metrology and quantum sensing aim to use quantum properties to enhance measurement precision beyond what could be classically achieved. Here, we demonstrate how the analysis of the phase space structure of the classical limit of…
We consider three different approaches to analyze the quantum mechanical problems in multi-well potentials: i) the standard matrix diagonalization technique in the basis sets of harmonic oscillator eigenfunctions or plain waves; ii) the…
The main aim of this paper is to demonstrate the method called "the Bosonization of Nonlocal Currents" (BNC), used for calculations of bound states in a quark model, within the simplest relativistic quantum field model of two scalar fields…
We consider certain quantum spectral problems appearing in the study of local Calabi-Yau geometries. The quantum spectrum can be computed by the Bohr-Sommerfeld quantization condition for a period integral. For the case of small Planck…
We present a polymer quantization of the -lambda/r^2 potential on the positive real line and compute numerically the bound state eigenenergies in terms of the dimensionless coupling constant lambda. The singularity at the origin is handled…
Assuming Coulomb-like as well as confining scalar potential, we have solved Shr\"odinger equation perturbatively in $1/m_Q$ with a heavy quark mass $m_Q$. The lowest order equation is examined carefully. Mass levels are fitted with…
We consider an approach in which the usual wave function in the quadrature representation of mode j of the electromagnetic field is further quantized to produce a field operator. Since the electromagnetic field is already second quantized,…
We give an example in which it is possible to understand quantum statistics using classical concepts. This is done by studying the interaction of charged matter oscillators with the thermal and zeropoint electromagnetic fields…
Following Bekenstein's suggestion that the horizon area of a black hole should be quantized, the discrete spectrum of the horizon area has been investigated in various ways. By considering the quasinormal mode of a black hole, we obtain the…
The recently introduced scheme [20,21] is extended to propose an algebraic non-perturbative approach for the analytical treatment of Schr\"odinger equations with non-solvable potentials involving an exactly solvable potential form together…
Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…
We have developed a simple method to solve anharmonic oscillators equations. The idea of our method is mainly based on the partitioning of the potential curve into (n+1) small intervals, solving the Schr\"odinger equation in each…