相关论文: Band theory in the context of the Hamilton-Jacobi …
In this work, we investigate energy bands in a three dimensional simple cubic lattice of contact potential. The energy bands in the first Brillouin Zone are obtained with Ewald's summation method. In comparison with single point potential,…
Wave functions on periodic lattices are commonly described by Bloch band theory. Besides Abelian Bloch states labeled by a momentum vector, hyperbolic lattices support non-Abelian Bloch states that have so far eluded analytical treatments.…
In this paper we prove, by expressing the energy as a function of the wave propagation speed, it is highlighted the existence of an equivalent mass of the wave, as well as of an Einstein type relations between the energy and this mass.…
It is argued that there is a sensible way to define conditional probabilities in quantum mechanics, assuming only Bayes's theorem and standard quantum theory. These probabilities are equivalent to the ``weak measurement'' predictions due to…
The possibility of consistency between the basic quantum principles and reduction (wave function reduction) is reexamined. The mathematical description of an organized macroscopic device is constructed explicitly as a convenient tool for…
The energy of a quantum particle cannot be determined exactly unless there is an infinite amount of time in which to perform the measurement. This paper considers the possibility that $\Delta E$, the uncertainty in the energy, may be…
Variational (Rayleigh-Ritz) methods are applied to local quantum field theory. For scalar theories the wave functional is parametrized in the form of a superposition of Gaussians and the expectation value of the Hamiltonian is expressed in…
The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (nondispersive oscillating/spinning solitons), displaying simultaneous particle-like and…
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 $\beta'/\beta$…
The Helmholtz equation in one dimension, which describes the propagation of electromagnetic waves in effectively one-dimensional systems, is equivalent to the time-independent Schr\"odinger equation. The fact that the potential term…
We study the dynamics of a 1D Bloch electron subjected to a constant electric field. The periodic potential is supposed to be less singular than the $\delta $-like potential (Dirac comb). We give a rigorous proof of Ao's result \cite{Ao}…
The quark-gluon sea in the hadrons is considered as periodically correlated. Energy levels of Shrodinger equation with harmonic potential is used for describing of the spectrum of hadron masses. In the considered cases the effective…
The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…
In the theory of ergodic one-dimensional Schrodinger operators, ac spectrum has been traditionally expected to be very rigid. Two key conjectures in this direction state, on one hand, that ac spectrum demands almost periodicity of the…
We derive analytic expressions of the recursive solutions to the Schr\"{o}dinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately…
We study the behaviour of the expectation value of the acceleration of a particle in a one-dimensional periodic potential when an external homogeneous force is suddenly applied. The theory is formulated in terms of modified Bloch states…
The electronic band structure, describing the periodic dependence of electronic quantum states on lattice momentum in reciprocal space, is a fundamental concept in solid-state physics. However, it's only well-defined for static nuclei. To…
Free bosonic fields are investigated at a classical level by imposing their characteristic de Broglie periodicities as constraints. In analogy with finite temperature field theory and with extra-dimensional field theories, this…
In the present work the conditions appearing in the WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length…
In this paper we obtain the asymptotic formulas of arbitrary order for the Bloch eigenvalues and Bloch functions of the multidimensional polyharmonic operator with periodic, with respect to arbitrary lattice, potential. Then we prove that…