Related papers: Bounds on Schr\"odinger Energies
We show how to use boundary conditions to drive the evolution on a Quantum Mechanical system. We will see how this problem can be expressed in terms of a time-dependent Schr\"{o}dinger equation. In particular we will need the theory of…
We cast the quantum chemistry problem of computing bound states as that of solving a set of auxiliary eigenvalue problems for a family of parameterized compact integral operators. The compactness of operators assures that their spectrum is…
By the use of the variational method with exponential trial functions the upper and lower bounds of energy are calculated for a number of non-relativistic three-body Coulomb and nuclear systems. The formulas for calculation of upper and…
We present a scheme for controlling the state of a quantum system by modifying the boundary conditions. This constitutes an infinite-dimensional control problem. We provide conditions for the existence of solutions of the dynamics and prove…
We construct energy-dependent potentials for which the Schroedinger equations admit solu- tions in terms of exceptional orthogonal polynomials. Our method of construction is based on certain point transformations, applied to the equations…
A control problem with terminal overdetermination is considered for the higher order nonlinear Schr\"odinger equation on a bounded interval. The boundary condition on the space derivative is chosen as the control. Results on global…
Firstly, a systematic procedure is derived for obtaining three-dimensional bound-state equations from four-dimensional ones. Unlike ``quasi-potential approaches'' this procedure does not involve the use of delta-function constraints on the…
This paper presents a novel and efficient approach for the computation of energy eigenvalues in quantum semiconductor heterostructures. Accurate determination of the electronic states in these heterostructures is crucial for understanding…
An alternative approximation scheme has been used in solving the Schrodinger equation for the exponential-cosine-screened Coulomb potential. The bound state energ\i es for various eigenstates and the corresponding wave functions are…
Exact solutions of time-dependent Schr\"odinger equation in presence of time-dependent potential is defined by point transformation and separation of variables. Energy and Heisenberg uncertainty relation are pursued for time-independent…
We solve the one-dimensional Schr\"odinger equation for the bound states of two potential models with a rich structure as shown by their "spectral phase diagram". These potentials do not belong to the well-known class of exactly solvable…
An alternative approximation scheme has been used in solving the Schrodinger equation to the more general case of exponential screened Coulomb potential, V(r)=-(a/r)\[1+(1+br)e^{-2br}]. The bound state energies of the 1s, $2s, and…
The formulation of the eigenvalue problem for the Schr\"odinger equation is studied, for the numerical solution a new approach is applied. With the usual exponentially rising free-state asymptotical behavior, and also with a first order…
We propose a new method to obtain approximate solutions for the Schr\"{o}dinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows in many cases to find analytical…
We establish quantum dynamical lower bounds for discrete one-dimensional Schr\"odinger operators in situations where, in addition to power-law upper bounds on solutions corresponding to energies in the spectrum, one also has lower bounds…
Transition states or quantum states of zero energy appear at the boundary between the discrete part of the spectrum of negative energies and the continuum part of positive energy states. As such, transition states can be regarded as a…
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…
Quasiclassical solution of the three-dimensional Schredinger's equation is given. The existence of nonzero minimal angular momentum M_0 = \hbar /2 is shown, which corresponds to the quantum fluctuations of the angular momentum and…
We consider the problem of energy-mass transfer from scattering to bound states for a one body quantum system under the action of a time dependent point interaction. Under suitable assumptions on the initial state of the particle, we prove…
The prevalent role of force in traditional quantum mechanics is outlined, with special reference to approximate calculations for stationary states. It will be explored how far this force concept can be made useful in the concerned area. The…