Related papers: Obtaining Hydrogen energy wave functions using the…
It is well-known that quantum mechanics admits two distinct evolutions: the unitary evolution, which is deterministic and well described by the Schr\"{o}dinger equation, and the collapse of the wave function, which is probablistic,…
Schrodinger path to the quantum mechanical wave equation was heuristic and guided more by physical intuition than formal deduction. Here we derive the Schrodinger equation for the particle wave function, assuming that it has a meaning of…
A solution of the two-dimensional Schr\"odinger equation with Pauli-Fierz Hamiltonian and trigonometric double-well potential is obtained within the framework of the first-order of adiabatic approximation. The case of vibrational strong…
A non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of Hydrogen atom are exactly same as the Dirac theory. The theory accounts for the energy due to…
The relativistic energies and widths of hydrogen-like ions exposed to the uniform electric field are calculated. The calculations are performed for the ground and lowest excited states using the complex scaling technique in combination with…
Effective interactions that fit the low energy p-$^3$He experimental data have been constructed. They are based on the Resonating Group Method and a modified Orthogonality Condition Model in which Pauli and partly Pauli forbidden states are…
We calculate the energy of a homogeneous one component plasma and find that the energy is lower for correlated motions of the particles as compared to uncorrelated motion. Our starting point is the conserved approximately relativistic…
We examine the mechanism for generating a mass for a U(1) vector field introduced by Stueckelberg. First, it is shown that renormalization of the vector mass is identical to the renormalization of the vector field on account of gauge…
In this paper, the conformable Schrodinger equation for hydrogen atom with given conformable potential is solved. The conformable wave functions and energy levels are obtained, and the traditional energy levels and wave function for…
Integral transforms arising from the separable solutions to the Helmholtz differential equation are presented. Pairs of these integral transforms are related via Plancherel theorem and, ultimately, any of these integral transforms may be…
The Fourier component of the potential energy of interaction of an atom with an atom is represented as a polynomial of the fourth degree from the atomic form factor. A numerical calculation was performed for the atomic form factor in the…
A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, discrete, homogeneous chains with a general power-law contact interaction is studied. For this wave equation,…
We study the space and properties of global and local observables for radiation emitted in the scattering of a massive scalar field in gauge and gravitational plane-wave backgrounds, in both the quantum and classical theory. We first…
We present a detailed derivation of the continuity, Euler, and energy balance equations from many particle Schrodinger equation. Interparticle interaction is explicitly considered as the Coulomb interaction. We show the QHD equations in a…
A remarkable mathematical property -- somehow hidden and recently rediscovered -- allows obtaining the eigenvectors of a Hermitian matrix directly from their eigenvalues. That opens the possibility to get the wavefunctions from the…
The irreducible representations of the extended Galilean group are used to derive infinite sets of symmetric and asymmetric second-order differential equations with constant coeffcients. All derived equations are local and their Lagrangians…
We consider bipartite quantum systems that are described completely by a state vector $|\Psi(t)>$ and the fully deterministic Schr\"odinger equation. Under weak constraints and without any artificially introduced decoherence or…
We consider quantum systems which interact strongly with a rapidly varying environment and derive a Schrodinger-like equation which describes the time evolution of the average wave function. We show that the corresponding Hamiltonian can be…
Bose-Einstein condensates with their superfluidity property provide an interesting parallel to classical fluids. Due to the Kolmogorov spectrum of homogeneous turbulence the statistics of the incompressible velocity field is of great…
The energy spectrum of the Coulomb potential with minimal length commutation relations $[X_i, P_j] = i\hbar\{\delta_{ij}(1+\beta P^2) + \beta'P_iP_j\}$ is determined both numerically and perturbatively for arbitrary values of $\beta'/\beta$…