Accessing Position Space Wave Functions in Band Structure Calculations of Periodic Systems─A Generalized, Adapted Numerov Implementation for One-, Two-, and Three-Dimensional Quantum Problems.

In this work, a generalized, adapted Numerov implementation capable of determining band structures of periodic quantum systems is outlined. Based on the input potential, the presented approach numerically solves the Schrödinger equation in position space at each momentum space point. Thus, in addition to the band structure, the method inherently provides information about the state functions and probability densities in position space at each momentum space point considered. The generalized, adapted Numerov framework provided reliable estimates for a variety of increasingly complex test suites in one, two, and three dimensions. The accuracy of the proposed methodology was benchmarked against results obtained for the analytically solvable Kronig-Penney model. Furthermore, the presented numerical solver was applied to a model potential representing a 2D optical lattice being a challenging application relevant, for example, in the field of quantum computing.

From vibrational spectroscopy and quantum tunnelling to periodic band structures - a self-supervised, all-purpose neural network approach to general quantum problems.

In this work, a feed-forward artificial neural network (FF-ANN) design capable of locating eigensolutions to Schrödinger's equation via self-supervised learning is outlined. Based on the input potential determining the nature of the quantum problem, the presented FF-ANN strategy identifies valid solutions solely by minimizing Schrödinger's equation encoded in a suitably designed global loss function. In addition to benchmark calculations of prototype systems with known analytical solutions, the outlined methodology was also applied to experimentally accessible quantum systems, such as the vibrational states of molecular hydrogen H2 and its isotopologues HD and D2 as well as the torsional tunnel splitting in the phenol molecule. It is shown that in conjunction with the use of SIREN activation functions a high accuracy in the energy eigenvalues and wavefunctions is achieved without the requirement to adjust the implementation to the vastly different range of input potentials, thereby even considering problems under periodic boundary conditions.

A 3-in-1 Hand-Held Ambient Mass Spectrometry Interface for Identification and 2D Localization of Chemicals on Surfaces.

Desorption electrospray ionization (DESI), easy ambient sonic-spray ionization (EASI) and low-temperature plasma (LTP) ionization are powerful ambient ionization techniques for mass spectrometry. However, every single method has its limitation in terms of polarity and molecular weight of analyte molecules. After the miniaturization of every possible component of the different ion sources, we finally were able to embed two emitters and an ion transfer tubing into a small, hand-held device. The pen-like interface is connected to the mass spectrometer and a separate control unit via a bundle of flexible tubing and cables. The novel device allows the user to ionize an extended range of chemicals by simple switching between DESI, voltage-free EASI, or LTP ionization as well as to freely move the interface over a surface of interest. A mini camera, which is mounted on the tip of the pen, magnifies the desorption area and enables a simple positioning of the pen. The interface was successfully tested using different types of chemicals, pharmaceuticals, and real life samples. Moreover, the combination of optical data from the camera module and chemical data obtained by mass analysis facilitates a novel type of imaging mass spectrometry, which we name "interactive mass spectrometry imaging (IMSI)".