相关论文: Band theory in the context of the Hamilton-Jacobi …
Standard derivations of ``time-independent perturbation theory'' of quantum mechanics cannot be applied to the general case where potentials are energy dependent or where the inverse free Green function is a non-linear function of energy.…
The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…
We show that two tight binding electrons that repel may form a bounded pair in two dimensions. The paired states form a band with energies that scale like the strength of the interaction potential. By applying an electric field we show that…
We study the low energy part of the nucleon and $\Delta$ spectra by solving the Schr\"{o}dinger equation for the three-quark system in the hyperspherical harmonic approach. The quark-quark hamiltonian considered includes, besides the usual…
We study the energy spectrum and the quantized Hall conductance of electrons in a two-dimensional periodic potential with perpendicular magnetic field WITHOUT neglecting the coupling of the Landau bands. Remarkably, even for weak Landau…
We present a unified field theory of wave and particle in quantum mechanics. This emerges from an investigation of three weaknesses in the de Broglie-Bohm (deBB) theory: its reliance on the quantum probability formula to justify the…
y formally diagonalizing with accuracy $\hbar$ the Hamiltonian of electrons in a crystal subject to electromagnetic perturbations, we resolve the debate on the Hamiltonian nature of semiclassical equations of motion with Berry-phase…
According to de Broglie, temperature plays a basic role in quantum Hamilton-Jacobi theory. Here we show that a possible dependence on the temperature of the integration constants of the relativistic quantum Hamilton-Jacobi may lead to…
The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact…
We pursue a low-wavenumber, second-order homogenized solution of the time-harmonic wave equation at both low and high frequency in periodic media with a source term whose frequency resides inside a band gap. Considering the wave motion in…
It is argued that the topological approach to the (anti-)symmetrisation condition for the quantum state of a collection of identical particles, defined in the `reduced' configuration space, is particularly natural from the perspective of de…
Cauchy initial value problem on a hyperboloid is proved to define a Hamiltonian system, provided the radiation data at null infinity are also taken into account, as a part of Cauchy data. The "Trautman-Bondi mass", supplemented by the…
We show that flat bands can be categorized into two distinct classes, that is, singular and nonsingular flat bands, by exploiting the singular behavior of their Bloch wave functions in momentum space. In the case of a singular flat band,…
Within the wave-packet semiclassical approach, the Bloch electron energy is derived to second order in the magnetic field and classified into gauge-invariant terms with clear physical meaning, yielding a fresh understanding of the complex…
We explore algebras associated with the hyperbolic band theory under a magnetic field for the first time. We define the magnetic Fuchsian group associated with a higher genus Riemann surface. By imposing the magnetic boundary conditions for…
A central object in the analysis of the water wave problem is the Dirichlet-Neumann operator. This paper is devoted to the study of its spectrum in the context of the water wave system linearized near equilibrium in a domain with a variable…
We show that the formulations of non-relativistic quantum mechanics can be derived from an extended least action principle. The principle extends the least action principle from classical mechanics by factoring in two assumptions. First,…
The celebrated Kronig-Penney model traditionally has been formulated with square well potentials representing atomic centres. Here, we use a slightly more realistic potential, the truncated harmonic oscillator, in lieu of square well…
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…
The behavior of monochromatic electromagnetic waves in stationary media is shown to be ruled by a frequency dependent function, which we call Wave Potential, encoded in the structure of the Helmholtz equation. Contrary to the common belief…