On the Nature of Unrestricted Orbitals in Variational Active Space Wave Functions

2006 ◽  
Vol 110 (32) ◽  
pp. 9915-9920 ◽  
Author(s):  
Gregory J. Beran ◽  
Martin Head-Gordon
Keyword(s):  
Wave Functions ◽  
Active Space ◽  
Space Wave

scholarly journals Precision Measurement of the Position-Space Wave Functions of Gravitationally Bound Ultracold Neutrons

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Y. Kamiya ◽  
G. Ichikawa ◽  
S. Komamiya
Keyword(s):  
Quantum Mechanics ◽  
Particle Physics ◽  
Bound States ◽  
Wave Functions ◽  
Recent Measurement ◽  
Ultracold Neutrons ◽  
Neutron Guide ◽  
Position Space ◽  
Position Sensitive Detectors ◽  
Space Wave

Gravity is the most familiar force at our natural length scale. However, it is still exotic from the view point of particle physics. The first experimental study of quantum effects under gravity was performed using a cold neutron beam in 1975. Following this, an investigation of gravitationally bound quantum states using ultracold neutrons was started in 2002. This quantum bound system is now well understood, and one can use it as a tunable tool to probe gravity. In this paper, we review a recent measurement of position-space wave functions of such gravitationally bound states and discuss issues related to this analysis, such as neutron loss models in a thin neutron guide, the formulation of phase space quantum mechanics, and UCN position sensitive detectors. The quantum modulation of neutron bound states measured in this experiment shows good agreement with the prediction from quantum mechanics.

scholarly journals Multi-reference Approach to the Computation of Double-Core-Hole Spectra

2021 ◽  
Author(s):  
Bruno Nunes Cabral Tenorio ◽  
Piero Decleva ◽  
Sonia Coriani
Keyword(s):  
Small Molecules ◽  
Ground State ◽  
Binding Energies ◽  
Wave Functions ◽  
Correlation Effects ◽  
Core Hole ◽  
Active Space ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

Double-Core Hole (DCH) states of small molecules are assessed with the restricted<br>active space self-consistent field (RASSCF) and multi-state restricted active space perturbation<br>theory of second order (MS-RASPT2) approximations. To ensure an unbiased<br>description of the relaxation and correlation effects on the DCH states, the neutral<br>ground state and DCH wave functions are optimized separately, whereas the spectral<br>intensities are computed with a biorthonormalized set of molecular orbitals within the<br>state-interaction (SI) approximation. Accurate shake-up satellites binding energies and<br>intensities of double-core-ionized states (K<sup>-2</sup>) are obtained for H<sub>2</sub>O, N<sub>2</sub>, CO and C<sub>2</sub>H<sub>2n</sub><br>(n=1–3). The results are analyzed in details and show excellent agreement with recent<br>experimental data.

Phase-Space Wave Functions of Harmonic Oscillator in Nanomaterials

2011 ◽  
Vol 233-235 ◽  
pp. 2154-2157
Author(s):  
Jun Lu
Keyword(s):  
Wave Function ◽  
Phase Space ◽  
Harmonic Oscillator ◽  
Wave Functions ◽  
Quantum Phase ◽  
Space Representation ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Phase Space Representation ◽  
Space Wave

In this paper, we solve the rigorous solutions of the stationary Schrödinger equations for the harmonic oscillator in nanomaterials within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. We obtain the phase-space eigenfunctions of the harmonic oscillator. We also discuss the character of wave function and the “Fourier-like” projection transformations in phase space.

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