Visualizing classical periodic orbits from the quantum energy spectrum via the Fourier transform: Simple infinite well examples

1997 ◽  
Vol 65 (12) ◽  
pp. 1167-1175 ◽  
Author(s):  
Richard W. Robinett
Keyword(s):  
Fourier Transform ◽  
Energy Spectrum ◽  
Periodic Orbits ◽  
Quantum Energy ◽  
The Fourier Transform

Periodic orbits from the quantum energy spectrum of the wedge billiard

1992 ◽  
Vol 69 (11) ◽  
pp. 1640-1643 ◽  
Author(s):  
T. Szeredi ◽  
D. A. Goodings
Keyword(s):  
Energy Spectrum ◽  
Periodic Orbits ◽  
Quantum Energy

scholarly journals From classical periodic orbits in integrable $ \pi$-rational billiards to quantum energy spectrum

2019 ◽  
Vol 134 (6) ◽  
Author(s):  
Subhasis Panda ◽  
Sabyasachi Maulik ◽  
Somdeb Chakraborty ◽  
S. Pratik Khastgir
Keyword(s):  
Energy Spectrum ◽  
Periodic Orbits ◽  
Quantum Energy

LOCALIZED ELECTRONIC STATES IN A TERNARY QUASIPERIODIC MODEL

2000 ◽  
Vol 14 (04) ◽  
pp. 435-448
Author(s):  
PEIQIN ZHOU ◽  
XIUJUN FU ◽  
YOUYAN LIU
Keyword(s):  
Fourier Transform ◽  
Energy Spectrum ◽  
Disordered Systems ◽  
Lattice Structure ◽  
Electronic States ◽  
Pure Point ◽  
One Dimensional ◽  
Second Moment ◽  
The Fourier Transform ◽  
The One

The one-dimensional ternary sequence generated by the substitutions S→M,M→L,L→LS is generally called SML quasiperiodic model [Phys. Rev.B43, 13240 (1991)], the electronic localization of which is studied. For this model, the Fourier transform, the b and -width dependence on site number, the second moment and multifractal behaviors of wavefunctions are investigated. It is found that the lattice structure is quasiperiodic, but the energy spectrum is of pure point and the electronic states are all localized, which exhibits the characteristic of disordered systems.

scholarly journals Простой численный метод определения энергетического спектра носителей заряда в полупроводниковых гетероструктурах

2018 ◽  
Vol 44 (6) ◽  
pp. 17
Author(s):  
Г.Ф. Глинский
Keyword(s):  
Fourier Transform ◽  
Energy Spectrum ◽  
Quantum Wells ◽  
Periodic Potential ◽  
Wave Functions ◽  
Charge Carriers ◽  
Semiconductor Heterostructures ◽  
Mass Approximation ◽  
The Fourier Transform ◽  
Envelope Functions

AbstractA simple numerical method for determining the energy spectrum and wave functions of charge carriers in semiconductor heterostructures (quantum wells, wires, dots, and superlattices) is proposed that employs the effective mass approximation in the general case of multiband kp Hamiltonian corresponding to the Γ point of the Brillouin zone. The method is based on the Fourier transform for structures with periodic potential. For single heterostructures, this periodicity is introduced artificially. In the framework of the proposed approach, the effective matrix Hamiltonian of a heterostructure can be written in two unitarily-equivalent a - and k -representations. As an example, single-band kp models of a heterostructure with one parabolic, triangular, or rectangular quantum well are considered and the influence of interfacial kp corrections on the behavior of envelope functions at sharp heteroboundaries is studied.

The infrared spectrum of H2S from 1 to 5 μm

1994 ◽  
Vol 72 (11-12) ◽  
pp. 989-1000 ◽  
Author(s):  
Alexander D. Bykov ◽  
Olga V. Naumenko ◽  
Maxim A. Smirnov ◽  
Leonid N. Sinitsa ◽  
Linda R. Brown ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Energy Spectrum ◽  
Infrared Spectrum ◽  
Energy Levels ◽  
Local Mode ◽  
Fourier Transform Spectrometer ◽  
National Observatory ◽  
The Fourier Transform ◽  
High Degree ◽  
First Time

The absorption spectra of H2S from 2000 to 11 147 cm−1 have been obtained with spectral resolutions of 0.006, 0.012, and 0.021 cm−1 using the Fourier transform spectrometer at Kitt Peak National Observatory. The transitions of 21 bands have been assigned for the first time and 9 others reanalyzed so that accurate energy levels, band origins, and rotational parameters could be determined. The analysis of these data revealed some remarkable features in the energy spectrum, e.g., fourfold clustering of rotational levels belonging to the symmetric and asymmetric components of local mode manifolds at a high degree of stretching excitation. This paper reports fitted vibrational parameters and predicted band origins of H232S up to 12 735 cm−1. It also presents the degenerate rotational constants and upper state energies of (301)–(202) and (311)–(212) at 1 μm as illustrations of clustering in the local mode limit.

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

Determination of starch crystallinity with the Fourier-transform terahertz spectrometer

2021 ◽  
Vol 262 ◽  
pp. 117928
Author(s):  
Shusaku Nakajima ◽  
Shuhei Horiuchi ◽  
Akifumi Ikehata ◽  
Yuichi Ogawa
Keyword(s):  
Fourier Transform ◽  
The Fourier Transform ◽  
Starch Crystallinity

Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lung-Hui Chen
Keyword(s):  
Fourier Transform ◽  
Entire Function ◽  
Convex Hull ◽  
Scattering Theory ◽  
Phase Retrieval ◽  
Indicator Function ◽  
Band Limited ◽  
The Fourier Transform ◽  
Complex Valued ◽  
Spectral Invariant

Abstract In this paper, we discuss how to partially determine the Fourier transform F ⁢ ( z ) = ∫ - 1 1 f ⁢ ( t ) ⁢ e i ⁢ z ⁢ t ⁢ 𝑑 t , z ∈ ℂ , F(z)=\int_{-1}^{1}f(t)e^{izt}\,dt,\quad z\in\mathbb{C}, given the data | F ⁢ ( z ) | {\lvert F(z)\rvert} or arg ⁡ F ⁢ ( z ) {\arg F(z)} for z ∈ ℝ {z\in\mathbb{R}} . Initially, we assume [ - 1 , 1 ] {[-1,1]} to be the convex hull of the support of the signal f. We start with reviewing the computation of the indicator function and indicator diagram of a finite-typed complex-valued entire function, and then connect to the spectral invariant of F ⁢ ( z ) {F(z)} . Then we focus to derive the unimodular part of the entire function up to certain non-uniqueness. We elaborate on the translation of the signal including the non-uniqueness associates of the Fourier transform. We show that the phase retrieval and magnitude retrieval are conjugate problems in the scattering theory of waves.

Sign in / Sign up

Export Citation Format

Share Document