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It is shown that by means of the approach based on the Quantum Hamilton-Jacobi equation, it is possible to modify the WKB expressions for the energy levels of quantum systems, when incorrect, obtaining exact WKB-like formulae. This extends…
This paper presents a new methodology for the solution of problems of two- and three-dimensional acoustic scattering (and, in particular, two-dimensional electromagnetic scattering) by obstacles and defects in presence an arbitrary number…
The dynamics of quantum systems under the adiabatic Hamiltonian has attracted attention not only in quantum control but also in a wide range of fields from condensed matter physics to high-energy physics because of its non-perturbative…
We present a set of exact system solutions to a model we developed to study wave function collapse in the quantum spin measurement process. Specifically, we calculated the wave function evolution for a simple harmonic oscillator of spin…
Higher-order WKB methods are used to investigate the border between the solvable and insolvable portions of the spectrum of quasi-exactly solvable quantum-mechanical potentials. The analysis reveals scaling and factorization properties that…
The energy levels of quantum systems are determined by quantization conditions. For one-dimensional anharmonic oscillators, one can transform the Schrodinger equation into a Riccati form, i.e., in terms of the logarithmic derivative of the…
The Born--Oppenheimer approximation is the standard tool for the study of molecular systems. It is founded on the observation that the energy scale of the electron dynamics in a molecule is larger than that of the nuclei. A very similar…
The nodal structure of bound-state wave functions for one-dimensional quantum systems with quartic energy-momentum dispersion and polynomial potentials is analysed by using the semiclassical approximation and variational approach. For…
In this work we analyze the variational problem emerging from the Gutzwiller approach to strongly correlated systems. This problem comprises the two main steps: evaluation and minimization of the ground state energy $W$ for the postulated…
Following our previous study of the Bohr-Sommerfeld (B-S) quantization condition for one-dimensional case (del Valle \& Turbiner (2021) \cite{First}), we extend it to $d$-dimensional power-like radial potentials. The B-S quantization…
We forecast the constraints on both Hu-Sawicki model and Bertschinger-Zukin model of modified gravity within the Parameterized Post-Friedmann (PPF) formalism for the Planck satellite experiment by performing the joint analysis of…
The one-dimensional Schr\"odinger equation with symmetric trigonometric double-well potential is exactly solved via angular prolate spheroidal function. Although it is inferior compared with multidimensional counterparts and its limitations…
This paper presents the derivation of Schwinger's gauge invariant result of $Im \cal{L}_{eff}$ upto one loop approximation, for particle production in an uniform electric field through the method of complex trajectory WKB approximation…
We have studied wavepacket dynamics in the Razavy hyperbolic double-well (DW) potential which is coupled to a harmonic oscillator (HO) by linear and quadratic interactions. Taking into account the lowest two states of DW and $(N+1)$ states…
The Differential Transfer Matrix Method is extended to the complex plane, which allows dealing with singularities at turning points. The result for real-valued systems are simplified and a pair of basis functions is found. These bases are a…
We propose a variational perturbation method based on the observation that eigenvalues of each parity sector of both the anharmonic and double-well oscillators are approximately equi-distanced. The generalized deformed algebra satisfied by…
We study the spectral problem in deformed supersymmetric quantum mechanics with polynomial superpotential by using the exact WKB method and the TBA equations. We apply the ODE/IM correspondence to the Schr\"odinger equation with an…
We have considered optical beams with phase singularity and experimentally verified that these beams, although being classical, have properties of two mode entanglement in quantum states. We have observed the violation of Bell's inequality…
The WKB approximation of geometrical optics is widely used in plasma physics, quantum mechanics and reduced wave modeling in general. However, it is well-known that the approximation breaks down at focal and turning points. In this work we…
New time dependent Wigner functions for the quantum harmonic oscillator have been obtained in this work. The Moyal equation for the harmonic oscillator has been presented as the wave equation of a 2D membrane in the phase plane. The values…