Related papers: Bounds on Schr\"odinger Energies
At the lower edge of the energy continuum the birth of an isolated quantum bound state is studied as caused by an infinitesimally small change of the interaction. In our model a single, asymptotically free massive quantum particle is…
We present an approach to quantum dynamical lower bounds for discrete one-dimensional Schr\"odinger operators which is based on power-law bounds on transfer matrices. It suffices to have such bounds for a nonempty set of energies. We apply…
An exact quantization rule for the bound states of the one-dimensional Schr\"{o}dinger equation is presented and is generalized to the three-dimensional Schr\"{o}dinger equation with a spherically symmetric potential.
We provide a leading order semiclassical asymptotics of the energy of bound states for magnetic Neumann Schr\"odinger operators in two dimensional (exterior) domains with smooth boundaries. The asymptotics is valid all the way up to the…
We study the problem of the boundary conditions in the numerical simulation of closed and open quantum systems, described by a Schr\"odinger equation. On one hand, we show that a closed quantum system is defined by local boundary…
An upgraded concept of solvability of Schr\"{o}dinger-type equations is proposed. In a broader methodical context of non-perturbative quantum theory the innovation involves potentials which are piece-wise analytic yielding differential…
We develop a computationally and numerically efficient method to calculate binding energies and corresponding wave functions of quantum mechanical three-body problems in low dimensions. Our approach exploits the tensor structure of the…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However…
This dissertation presents and prove the viability of a non-standard method for controlling the state of a quantum system by modifying its boundary conditions instead of relying on the action of external fields. The standard approach to…
Upper and lower bounds are established for the survival probability $|<\psi(0)|\psi(t)>|^{2}$ of a quantum state, in terms of the energy moments $<\psi(0)|H^{n}|\psi(0)>$. Introducing a cut-off in the energy generally enables considerable…
We propose an approximate solution of the time-dependent Schr\"odinger equation using the method of stationary states combined with a variational matrix method for finding the energies and eigenstates. We illustrate the effectiveness of the…
This paper presents an energy estimate in terms of the total variation of the control for bilinear infinite dimensional quantum systems with unbounded potentials. These estimates allow a rigorous construction of propagators associated with…
An efficient new method is presented to calculate the quantum transports using periodic boundary conditions. This new method is based on a method we developed previously, but with an essential change in solving the Schrodinger's equation.…
The energy levels of the ground states of the three-particle and four-particle bound states of leptons in quantum electrodynamics are calculated. For the calculation, the variational method with Gaussian basis functions is used. The…
Active control of quantum systems enables diverse applications ranging from quantum computation to manipulation of molecular processes. Maximum speeds and related bounds have been identified from uncertainty principles and related…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the…
Exact solution of Schrodinger equation for the Mie potential is obtained for an arbitrary angular momentum. The energy eigenvalues and the corresponding wavefunctions are calculated by the use of the Nikiforov-Uvarov method. Wavefunctions…
The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum…