Using the symmetries of the three-dimensional Paul trap, we derive the solutions of the time-dependent Schrodinger equation for this system, in both Cartesian and cylindrical coordinates. Our symmetry calculations provide insights that are not always obvious from the conventional viewpoint.

Recently reported computations have been extended to give ten more decimals of accuracy in the ground state energy of the Schrodinger equation for the idealized Helium atom. With the F basis-Hylleraas coordinates with negative powers and a logarithm of s-carried to the fiftieth order (N = 24,099 terms) we find the eigenvalue

The interactive behaviors between transverse magnetic fields and axial loads of a magnetoelastic ME beam subjected to general boundary conditions are investigated. In particular, the instability criterion for the magneto-mechanical buckling problem is intricately discussed based on the structure characteristics and the initial conditions. The equation of motion for the proposed physical model i...

We present the theories used in solid-state nuclear magnetic resonance and the expansion schemes used as numerical integrators for solving the time dependent Schrodinger Equation. We highlight potential future theoretical and numerical directions in solid-state nuclear magnetic resonancesuch as the Chebychev expansion and the transformation of Cayley.

Quantum Monte Carlo estimates of the spectrum of rotationally invariant states of noble gas clusters suggest interdimensional degeneracy in N-1 and N+1 spatial dimensions. We derive this property by mapping the Schrodinger eigenvalue problem onto an eigenvalue equation in which D appears as a continuous variable. We discuss implications for quantum Monte Carlo and dimensional scaling methods.

A coherent atomic beam splitter can be realized using the transient dynamics of a chaotic system. We have experimentally observed such an effect using ultracold rubidium atoms. Our experimental results are in good agreement with numerical simulations of the Schrodinger equation for the system.

In scientific machine learning, regression networks have been recently applied to approximate solution maps (e.g., the potential-ground state map of Schrodinger equation). this paper, we aim...

We prove the existence and uniqueness of smooth solutions with large initial data for a system equations modeling interaction short waves, governed by nonlinear Schrodinger equation, an...