How to prepare quantum states that follow classical paths

We present an alternative quantization procedure for the one-dimensional non-relativistic quantum mechanics. We show that, for the case of a free particle and a particle in a box, the complete classical and quantum correspondence can be obtained using this formulation. The resulting wave packets do not disperse and strongly peak on the classical paths. Moreover, for the case of the free particle, they satisfy minimum uncertainty relation.Comment: 10 pages, 3 figures, to appear in Europhysics Letter

Optimized basis expansion as an extremely accurate technique for solving time-independent Schr\"odinger equation

We use the optimized trigonometric finite basis method to find energy eigenvalues and eigenfunctions of the time-independent Schrodinger equation with high accuracy. We apply this method to the quartic anharmonic oscillator and the harmonic oscillator perturbed by a trigonometric anharmonic term as not exactly solvable cases and obtain the nearly exact solutions.Comment: 11 pages, 4 figure

Generalized Uncertainty Principle and the Ramsauer-Townsend Effect

The scattering cross section of electrons in noble gas atoms exhibits a minimum value at electron energies of approximately 1eV. This is the Ramsauer-Townsend effect. In this letter, we study the Ramsauer-Townsend effect in the framework of the Generalized Uncertainty Principle.Comment: 11 pages, 3 figure

Modification of Coulomb's law in closed spaces

We obtain a modified version of Coulomb's law in two- and three-dimensional closed spaces. We demonstrate that in a closed space the total electric charge must be zero. We also discuss the relation between total charge neutrality of a isotropic and homogenous universe to whether or not its spatial sector is closed.Comment: 11 pages, 3 figure

Using Spectral Method as an Approximation for Solving Hyperbolic PDEs

We demonstrate an application of the spectral method as a numerical approximation for solving Hyperbolic PDEs. In this method a finite basis is used for approximating the solutions. In particular, we demonstrate a set of such solutions for cases which would be otherwise almost impossible to solve by the more routine methods such as the Finite Difference Method. Eigenvalue problems are included in the class of PDEs that are solvable by this method. Although any complete orthonormal basis can be used, we discuss two particularly interesting bases: the Fourier basis and the quantum oscillator eigenfunction basis. We compare and discuss the relative advantages of each of these two bases.Comment: 19 pages, 14 figures. to appear in Computer Physics Communicatio

Signature change from Schutz's canonical quantum cosmology and its classical analogue

We study the signature change in a perfect fluid Friedmann-Robertson-Walker quantum cosmological model. In this work the Schutz's variational formalism is applied to recover the notion of time. This gives rise to a Schrodinger-Wheeler-DeWitt equation with arbitrary ordering for the scale factor. We use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation value of the scale factor which coincides with the ontological interpretation. We show that these solutions exhibit signature transitions from a finite Euclidean to a Lorentzian domain. Moreover, such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid is present.Comment: 15 pages, 4 figures, to appear in PR