Related papers: 3D Quantum Trajectories. Quantum orbits of the Hyd…
It is shown that for any given quantum system evolving unitarily with the Hamiltonian, $\hat{H} = \hat{\bf p}^2/(2m) + U({\bf q})$, [bold letters denote $D$-dimensional ($D \geqslant 3$) vectors] and with a sufficiently smooth potential…
The paper deals with Hawking radiation related to non-static spherically symmetric black hole. Quantum corrections are incorporated using Hamilton-Jacobi method beyond semi-classical approximation. It is found that different order…
The existence of a maximal acceleration for massive objects was conjectured by Caianiello 30 years ago based on the Heisenberg uncertainty relations. Many consequences of this hypothesis have been studied, but until now, there has been no…
We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying…
In this paper, we derive equations of motion for the normal-order, the symmetric-order and the antinormal-order quantum characteristic functions, applicable for general Hamiltonian systems. We do this by utilizing the `characteristic form'…
In this thesis the quantum Hamilton - Jacobi (QHJ) formalism is used for (i) potentials which exhibit different spectra for different ranges of the potential parameters, (ii) exactly solvable (ES) periodic potentials (iii) quasi - exactly…
Quantum canonical transformations have attracted interest since the beginning of quantum theory. Based on their classical analogues, one would expect them to provide a powerful quantum tool. However, the difficulty of solving a nonlinear…
For the description of the transport of electrons across a quantum dot, which is tunnel coupled to leads at different chemical potentials, it is usual to assume that the total Hamiltonian of the composite system of the leads and the quantum…
Quantum systems in specific regimes display recurrences at the period of the periodic orbits of the corresponding classical system. We investigate the excited hydrogen atom in a magnetic field -- a prototypical system of 'quantum chaos' --…
The Hamilton-Jacobi equation (HJE) is one of the most elegant approach to Lagrangian systems such as geometrical optics and classical mechanics, establishing the duality between trajectories and waves and paving the way naturally for the…
Consider any stationary Schroedinger wave equation (SWE) solution $psi (x)$ for a particle. The corresponding PDF on position QTR{em}{x} of the particle is QTR{em}{p}$_{X}(x)=|psi (x)|^{2}$. There is a classical trajectory QTR{em}{x(t)} for…
The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum…
We show that the dynamics of a closed quantum system obeys the Hamilton variation principle. Even though quantum particles lack well-defined trajectories, their evolution in the Husimi representation can be treated as a flow of…
We investigate the effect of a quantised vibrational mode on electron tunneling through a chain of three quantum dots. The outer dots are coupled to voltage leads, but the position of the central dot is not rigidly fixed. Motion of the…
Hydrogen atom is studied as a quantum-classical hybrid system, where the proton is treated as a classical object while the electron is regarded as a quantum object. We use a well known mean-field approach to describe this hybrid hydrogen…
The quantum mechanical motion of the atomic nuclei is considered over a single- or a multi-dimensional subspace of electronic states which is separated by a gap from the rest of the electronic spectrum over the relevant range of nuclear…
A hierarchical ordering is demonstrated for the periodic orbits in a strongly coupled multidimensional Hamiltonian system, namely the hydrogen atom in crossed electric and magnetic fields. It mirrors the hierarchy of broken resonant tori…
The hydrogen atom theory is developed for the de Sitter and anti de Sitter spaces on the basis of the Klein-Gordon-Fock wave equation in static coordinates. In both models, after separation of the variables, the problem is reduced to the…
In this educational paper, we will discuss calculations on the hydrogen molecule both on classical and quantum computers. In the former case, we will discuss the calculation of molecular integrals that can then be used to calculate…
The Hamilton-Jacobi method is generalized, both, in classical and relativistic mechanics. The implications in quantum mechanics are considered in the case of Klein-Gordon equation. We find that the wave functions of Klein-Gordon theory can…