相关论文: A simple method to construct eigenset of single-ac…
This paper addresses the single-valued requirement for quantum wave functions when they are analytically continued in the spatial coordinates. This is particularly relevant for de Broglie-Bohm, hydrodynamic, or stochastic models of quantum…
We present a linear scaling formulation for the solution of the all-electron Coulomb problem in crystalline solids. The resulting method is systematically improvable and well suited to large-scale quantum mechanical calculations in which…
We formulate a three-dimensional semi-classical model to address triple and double ionization in three-electron atoms driven by intense infrared laser pulses. During time propagation, our model fully accounts for the Coulomb singularities,…
By their very nature, field-theoretical Hamiltonians are derived in momentum representation. To solve the corresponding integro-differential equations is more difficult than to solve the simpler differential equations in configuration space…
The ultimate miniaturization of electronic devices will likely require local and coherent control of single electronic wavefunctions. Wavefunctions exist within both physical real space and an abstract state space with a simple geometric…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
We study the numerical solution of the non-relativistic Schr\"{o}dinger equation for two-electron atoms in ground and excited S-states using pseudospectral (PS) methods of calculation. The calculation achieves convergence rates for the…
We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen in relativistic quantum mechanics. From mathematical viewpoint, the goal is equivalent to determination of the…
We present an efficient method for preparing the initial state required by the eigenvalue approximation quantum algorithm of Abrams and Lloyd. Our method can be applied when solving continuous Hermitian eigenproblems, e.g., the Schroedinger…
Time-periodic (Floquet) systems are one of the most interesting nonequilibrium systems. As the computation of energy eigenvalues and eigenstates of time-independent Hamiltonians is a central problem in both classical and quantum…
We discussed exact solutions of the Schroedinger equation for a two-dimensional parabolic confinement potential in a homogeneous external magnetic field. It turns out that the two-electron system is exactly solvable in the sense, that the…
First a set of coherent states a la Klauder is formally constructed for the Coulomb problem in a curved space of constant curvature. Then the flat-space limit is taken to reduce the set for the radial Coulomb problem to a set of hydrogen…
We outline a rigorous method which can be used to solve the many-body Schroedinger equation for a Coulomb interacting electronic system in an external classical magnetic field as well as a quantized electromagnetic field. Effects of the…
The one dimensional Schroedinger hydrogen atom is an interesting mathematical and physical problem to study bound states, eigenfunctions and quantum degeneracy issues. This 1D physical system gave rise to some intriguing controversy over…
We construct a general algorithm generating the analytic eigenfunctions as well as eigenvalues of one-dimensional stationary Schroedinger Hamiltonians. Both exact and quasi-exact Hamiltonians enter our formalism but we focus on quasi-exact…
Evaluating multi-center molecular integrals with Cartesian Gaussian-type basis sets has been a long-standing bottleneck in electronic structure theory calculation for solids and molecules. We have developed a vector-coupling and…
Experiments on atoms in intense laser pulses and the corresponding exact ab initio solutions of the time-dependent Schr\"odinger equation (TDSE) yield photoelectron spectra with low-energy features that are not reproduced by the otherwise…
Solution of the momentum space Schr\"odinger equation in the case of deformed fields is being addressed. In particular it is shown that a complete set of single particle states which includes bound, resonant and complex continuum states may…
We solve the quantum mechanical problem of a charged particle on S^2 in the background of a magnetic monopole for both bosonic and supersymmetric cases by constructing Hilbert space and realizing the fundamental operators obeying…
We improve the complex scaling method (CSM) to obtain virtual states, which were previously challenging in the conventional CSM. Our approach solves the Schr\"odinger equation in the momentum space as an eigenvalue problem by choosing the…