We study a general double Dirac delta potential to show that this is the simplest yet versatile s... more We study a general double Dirac delta potential to show that this is the simplest yet versatile solvable potential to introduce double wells, avoided crossings, resonances and perfect transmission (T = 1). Perfect transmission energies turn out to be the critical property of symmetric and antisymmetric cases wherein these discrete energies are found to correspond to the eigenvalues of Dirac delta potential placed symmetrically between two rigid walls. For well(s) or barrier(s), perfect transmission [or zero reflectivity, R(E)] at energy E = 0 is non-intuitive. However, earlier this has been found and called "threshold anomaly". Here we show that it is a critical phenomenon and we can have 0 ≤ R(0) < 1 when the parameters of the double delta potential satisfy an interesting condition. We also invoke zero-energy and zero curvature eigenstate (ψ(x) = Ax + B) of delta well between two symmetric rigid walls for R(0) = 0. We resolve that the resonant energies and the perfect transmission energies are different and they arise differently.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.
Practitioners spend significant amounts of time creating high-level design from requirements. Tho... more Practitioners spend significant amounts of time creating high-level design from requirements. Though there exist methodologies to describe and manage requirements and design artifacts, there is not yet an automated way to faithfully translate a requirement into a high-level design. While it is extremely difficult to generate design elements from free-form natural language due to its inherent ambiguity, it is possible to significantly improve the accuracy of the design from relatively structured and constrained natural language. In this paper we propose a technique to generate high-level class diagrams from a set of requirements, using a set of requirement-specific heuristics. In this approach, we leverage work we had previously done to first process a requirement statement to classify it into a requirement type, and then break it into various constituents. Depending on the requirement type and its constituents, our heuristics then discover a functional design comprising of coarse-grained modules, their relationships and responsibilities. We express the design as a UML class diagram in IBM rational software architect (RSA) format. Our preliminary investigation shows that the resulting class diagram is rich, and can be used by practitioners as a basis for further design.
We study a general double Dirac delta potential to show that this is the simplest yet versatile s... more We study a general double Dirac delta potential to show that this is the simplest yet versatile solvable potential to introduce double wells, avoided crossings, resonances and perfect transmission (T = 1). Perfect transmission energies turn out to be the critical property of symmetric and antisymmetric cases wherein these discrete energies are found to correspond to the eigenvalues of Dirac delta potential placed symmetrically between two rigid walls. For well(s) or barrier(s), perfect transmission [or zero reflectivity, R(E)] at energy E = 0 is non-intuitive. However, earlier this has been found and called "threshold anomaly". Here we show that it is a critical phenomenon and we can have 0 ≤ R(0) < 1 when the parameters of the double delta potential satisfy an interesting condition. We also invoke zero-energy and zero curvature eigenstate (ψ(x) = Ax + B) of delta well between two symmetric rigid walls for R(0) = 0. We resolve that the resonant energies and the perfect transmission energies are different and they arise differently.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.
Practitioners spend significant amounts of time creating high-level design from requirements. Tho... more Practitioners spend significant amounts of time creating high-level design from requirements. Though there exist methodologies to describe and manage requirements and design artifacts, there is not yet an automated way to faithfully translate a requirement into a high-level design. While it is extremely difficult to generate design elements from free-form natural language due to its inherent ambiguity, it is possible to significantly improve the accuracy of the design from relatively structured and constrained natural language. In this paper we propose a technique to generate high-level class diagrams from a set of requirements, using a set of requirement-specific heuristics. In this approach, we leverage work we had previously done to first process a requirement statement to classify it into a requirement type, and then break it into various constituents. Depending on the requirement type and its constituents, our heuristics then discover a functional design comprising of coarse-grained modules, their relationships and responsibilities. We express the design as a UML class diagram in IBM rational software architect (RSA) format. Our preliminary investigation shows that the resulting class diagram is rich, and can be used by practitioners as a basis for further design.
Uploads
Papers by Vibhu Sharma