Related papers: Universal Approach for Determining Multi-Dimension…
The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized…
Harmonic inversion is introduced as a powerful tool for both the analysis of quantum spectra and semiclassical periodic orbit quantization. The method allows to circumvent the uncertainty principle of the conventional Fourier transform and…
Anharmonicities provide a wealth of information about the vibrational dynamics, mode coupling and energy transfer within a polyatomic system. In this contribution we show how driven molecular dynamics trajectories can be used to extract…
We use vibrational dynamical mean-field theory (VDMFT) to study the vibrational structure of type-I clathrate solids, specifically X$_8$Ga$_{16}$Ge$_{30}$, where X=Ba,Sr. These materials are cage-like chemical structures hosting loosely…
We introduce the Anharmonic Oscillator Symmetry Model to describe vibrational excitations in molecular systems exhibiting high degree of symmetry. A systematic procedure is proposed to establish the relation between the algebraic and…
Electronic structure calculation of atoms and molecules, in the past few decades has largely been dominated by density functional methods. This is primarily due to the fact that this can account for electron correlation effects in a…
We construct a generalised expression for the normal ordering of (a+a^{\dagger})^{m} for integral values of m and use the result to study the quantum anharmonic oscillator problem in the Heisenberg approach. In particular, we derive…
Using the post-Gaussian trial functions, we calculate the variational solutions to the quantum-mechanical anharmonic oscillator. We evaluate not only the ground state but also some excited energies, and compare them with numerical results.
The construction of the Hamiltonian matrix \textbf{H} is an essential, yet computationally expensive step in \textit{ab-initio} device simulations based on density-functional theory (DFT). In homogeneous structures, the fact that a unit…
Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with…
We introduce a quantum information analysis of vibrational wave functions to understand complex vibrational spectra of molecules with strong anharmonic couplings and vibrational resonances. For this purpose, we define one- and two-modal…
Density functional theory (DFT) provides a theoretical framework for efficient and fairly accurate calculations of the electronic structure of molecules and crystals. The main features of density functional theory are described and DFT…
Here is presented an original program based on molecular Schrodinger equations. It is dedicated to target specific states of infrared vibrational spectrum in a very precise way with a minimal usage of memory. An eigensolver combined with a…
General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the…
Under the Franck-Condon approximation, we systematically validated the performance of density functional theory (DFT) and the effects of anharmonicity in simulating C/N/O K-edge vibrationally-resolved X-ray spectra of common diatomic…
The general theory of time-dependent frequency and time-dependent mass ('effective mass') is described.The general theory for time-dependent harmonic- oscillator is applied in the present research for studying certain quantum effects in the…
Based on a quantum Langevin equation and its corresponding Hamiltonian within a c-number formalism we calculate the vibrational dephasing rate of a cubic oscillator. It is shown that leading order quantum correction due to anharmonicity of…
We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of…
The problem of the quantum harmonic oscillator is investigated in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero divisors. Starting with the commutator of the bicomplex position…
The generalized density matrix (GDM) method is used to calculate microscopically the parameters of the collective Hamiltonian. Higher order anharmonicities are obtained consistently with the lowest order results, the mean field…