Probability of tunneling through potential barriers in more than one dimension

1980 ◽  
Vol 45 (1) ◽  
pp. 886-894
Author(s):  
M. Yu. Sumetskii
Keyword(s):  
One Dimension ◽  
Potential Barriers

scholarly journals Penetration into potential barriers in several dimensions

1937 ◽  
Vol 163 (915) ◽  
pp. 606-610 ◽  
Keyword(s):  
Refractive Index ◽  
Jacobi Equation ◽  
One Dimension ◽  
Practical Application ◽  
One Dimensional ◽  
Potential Barriers ◽  
Separable Problems ◽  
Total Reflexion ◽  
Similar Approximation ◽  
Hamilton Jacobi Equation

It is well known that in regions in which the refractive index varies sufficiently slowly, Schrödinger’s equation can be very simply treated by using its connexion with Hamilton-Jacobi’s differential equation. It is also known that a similar approximation is possible in regions of slowly varying imaginary refractive index (total reflexion). For the latter case the method was developed in papers by Jeffreys (1924), Wentzel (1926), Brillouin (1926) and Kramers (1926). These papers discuss also the behaviour of the wave function in the neighbourhood of the limit between the regions of real and imaginary refractive index. But although the connexion with the Hamilton-Jacobi equation holds in any number of dimensions, this equation can be solved by elementary means only in one dimension (or for problems that can by separation be reduced to one dimension), and for this reason the practical application of the method has so far been limited to one-dimensional or separable problems. In the present paper we discuss the case of more than one dimension and show that certain very simple inequalities may be obtained.

Resonant Tunneling of Fast Solitons through Large Potential Barriers

2011 ◽  
Vol 63 (6) ◽  
pp. 1201-1219 ◽  
Author(s):  
Walid K. Abou Salem ◽  
Catherine Sulem
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Resonant Tunneling ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
One Dimension ◽  
Potential Barriers ◽  
Nonlinear Schrödinger ◽  
Large Potential

AbstractWe rigorously study the resonant tunneling of fast solitons through large potential barriers for the nonlinear Schrödinger equation in one dimension. Our approach covers the case of general nonlinearities, both local and Hartree (nonlocal).

Colloidal Quantum Dots of III-V Semiconductors

MRS Bulletin ◽  
1998 ◽  
Vol 23 (2) ◽  
pp. 24-30 ◽  
Author(s):  
Arthur J. Nozik ◽  
Olga I. Mićić
Keyword(s):  
Quantum Wells ◽  
Epitaxial Film ◽  
Energy Levels ◽  
Epitaxial Films ◽  
Charge Carriers ◽  
One Dimension ◽  
Potential Barriers ◽  
Semiconductor Structures ◽  
Barrier Region ◽  
De Broglie Wavelength

Quantization effects in semiconductor structures were first demonstrated in the early 1970s in III-V quantum wells; these structures consisted of a thin epitaxial film of a smaller bandgap (Eg) semiconductor (e.g., GaAs, Eg = 1.42 eV) sandwiched between two epitaxial films of a larger bandgap semiconductor (e.g., Al0.3Ga0.7As, Eg = 2.0 eV). The conduction- and valence-band offsets of the two semiconductor materials produce potential barriers for electrons and holes, respectively. The smaller bandgap semiconductor constitutes the quantum-well region and the larger bandgap material the potential barrier region. If the film of the smaller bandgap material is sufficiently thin (thickness less than the de-Broglie wavelength of the charge carriers, which typically requires thicknesses less than about 300 Å for III-V semiconductors), then the charge carriers are confined in one dimension by the potential barriers, and quantization of the energy levels for both electrons and holes can occur (Figure 1).

Reconstruction of Objects from their Projections Using Orthogonal Functions

1973 ◽  
Vol 31 ◽  
pp. 268-269
Author(s):  
Elrnar Zeitler
Keyword(s):  
Unit Area ◽  
Three Dimensional ◽  
One Dimension ◽  
Spatial Density ◽  
Dimensional Representation ◽  
Orthogonal Functions ◽  
Object A ◽  
Plane Normal ◽  
Dimensional Object ◽  
Spatial Density Distribution

Considering any finite three-dimensional object, a “projection” is here defined as a two-dimensional representation of the object's mass per unit area on a plane normal to a given projection axis, here taken as they-axis. Since the object can be seen as being built from parallel, thin slices, the relation between object structure and its projection can be reduced by one dimension. It is assumed that an electron microscope equipped with a tilting stage records the projectionWhere the object has a spatial density distribution p(r,ϕ) within a limiting radius taken to be unity, and the stage is tilted by an angle 9 with respect to the x-axis of the recording plane.

Quantitative Diameter Measurements of Chromatin and TMV Fibers in the Freeze-Dried State

1988 ◽  
Vol 46 ◽  
pp. 170-171
Author(s):  
B. D. Athey ◽  
A. L. Stout ◽  
M. F. Smith ◽  
J. P. Langmore
Keyword(s):  
Reliable Method ◽  
Fiber Diameter ◽  
Quantitative Agreement ◽  
One Dimension ◽  
Fiber Axis ◽  
Two Dimensional ◽  
Fiber Density ◽  
Variable Diameter ◽  
Freeze Dried ◽  
Expected Values

Although there is general agreement that Inactive chromosome fibers consist of helically packed nucleosomes, the pattern of packing is still undetermined. Only one of the proposed models, the crossed-linker model, predicts a variable diameter dependent on the length of DNA between nucleosomes. Measurements of the fiber diameter of negatively-stained and frozen- hydrated- chromatin from Thyone sperm (87bp linker) and Necturus erythrocytes (48bp linker) have been previously reported from this laboratory. We now introduce a more reliable method of measuring the diameters of electron images of fibrous objects. The procedure uses a modified version of the computer program TOTAL, which takes a two-dimensional projection of the fiber density (represented by the micrograph itself) and projects it down the fiber axis onto one dimension. We illustrate this method using high contrast, in-focus STEM images of TMV and chromatin from Thyone and Necturus. The measured diameters are in quantitative agreement with the expected values for the crossed-linker model for chromatin structure

Effect of CT-based attenuation correction on uptake ratios in skeletal SPECT

2007 ◽  
Vol 46 (01) ◽  
pp. 38-42 ◽  
Author(s):  
V. Schulz ◽  
I. Nickel ◽  
A. Nömayr ◽  
A. H. Vija ◽  
C. Hocke ◽  
...  
Keyword(s):  
Vertebral Body ◽  
Facet Joint ◽  
One Dimension ◽  
Patient Specific ◽  
Data Sets ◽  
Facet Joints ◽  
Lumbar Vertebral Body ◽  
Ct System ◽  
Ct Data ◽  
Attenuation Corrected

SummaryThe aim of this study was to determine the clinical relevance of compensating SPECT data for patient specific attenuation by the use of CT data simultaneously acquired with SPECT/CT when analyzing the skeletal uptake of polyphosphonates (DPD). Furthermore, the influence of misregistration between SPECT and CT data on uptake ratios was investigated. Methods: Thirty-six data sets from bone SPECTs performed on a hybrid SPECT/CT system were retrospectively analyzed. Using regions of interest (ROIs), raw counts were determined in the fifth lumbar vertebral body, its facet joints, both anterior iliacal spinae, and of the whole transversal slice. ROI measurements were performed in uncorrected (NAC) and attenuation-corrected (AC) images. Furthermore, the ROI measurements were also performed in AC scans in which SPECT and CT images had been misaligned by 1 cm in one dimension beforehand (ACX, ACY, ACZ). Results: After AC, DPD uptake ratios differed significantly from the NAC values in all regions studied ranging from 32% for the left facet joint to 39% for the vertebral body. AC using misaligned pairs of patient data sets led to a significant change of whole-slice uptake ratios whose differences ranged from 3,5 to 25%. For ACX, the average left-to-right ratio of the facet joints was by 8% and for the superior iliacal spines by 31% lower than the values determined for the matched images (p <0.05). Conclusions: AC significantly affects DPD uptake ratios. Furthermore, misalignment between SPECT and CT may introduce significant errors in quantification, potentially also affecting leftto- right ratios. Therefore, at clinical evaluation of attenuation- corrected scans special attention should be given to possible misalignments between SPECT and CT.

Patient feedback on a new method of consulting with the GP; an analysis of responses by users of online triage software

2018 ◽  
Vol 68 (suppl 1) ◽  
pp. bjgp18X696773
Author(s):  
Abi Eccles ◽  
Mike Hopper ◽  
Helen Atherton
Keyword(s):  
Free Text ◽  
Telephone Consultation ◽  
Face To Face ◽  
Potential Barriers ◽  
Online Consultation ◽  
Patient Feedback ◽  
Levels Of Use ◽  
Negative Perceptions ◽  
Context Dependent ◽  
Feedback Data

BackgroundOnline triage software is a new way to triage patients online that allows patients to describe their problem via an online form. A GP then contacts the patient to arrange either a face-to-face or telephone consultation.AimThis study aimed to explore use of online consultation software and gain insight into patients’ experiences of using online consultations, identifying potential barriers and facilitators to use.MethodThis is a mixed methods retrospective study analysing data about patient users and their associated feedback. Data from a sample of 5591 patients were quantitatively analysed to describe characteristics of users. 576 out of the 5591 users left free-text feedback comments on their experience of use. These were thematically analysed.ResultsThe highest levels of use were observed in 25–35-year olds and lowest from those aged >65. Key themes identified included convenience, consultation quality, appropriateness, resource-use and functionality. Within each, a range of subthemes were present representing both positive and negative perceptions, suggesting that experiences of using online triage varied and were often context-dependentConclusionThere are various advantages to online triage software, but these are context-dependent. Therefore, such applications should be offered as an additional way to contact the GP surgery, rather than a replacement for more established methods, to ensure appropriate and equal access for patients.

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