Dr. Edgardo Cheb-Terrab: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=15401
en-us2022 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 27 Jan 2022 17:00:30 GMTThu, 27 Jan 2022 17:00:30 GMTNew applications published by Dr. Edgardo Cheb-Terrabhttps://www.maplesoft.com/images/Application_center_hp.jpgDr. Edgardo Cheb-Terrab: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=15401
The hidden SO4 symmetry of the hydrogen atom
https://www.maplesoft.com/applications/view.aspx?SID=154764&ref=Feed
In this worksheet, we derive the SO(4) symmetry of the hydrogen atom and its energy spectrum, without explicitly solving Schrodinger’s equation, using the Maple Physics package. While this problem is well known [4], [5], its solution involves several steps manipulating expressions with tensorial quantum operators, including simplifying them by taking into account a combination of commutator rules and Einstein’s sum rule for repeated indices. Therefore, it is an excellent model to test the current status of Computer Algebra Systems (CAS) concerning this kind of quantum-and-tensor-algebra computations and to showcase the CAS technique. The presentation also shows two alternative patterns of steps that can be used for systematically tackling more complicated symbolic problems of this kind.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="The hidden SO4 symmetry of the hydrogen atom" style="max-width: 25%;" align="left"/>In this worksheet, we derive the SO(4) symmetry of the hydrogen atom and its energy spectrum, without explicitly solving Schrodinger’s equation, using the Maple Physics package. While this problem is well known [4], [5], its solution involves several steps manipulating expressions with tensorial quantum operators, including simplifying them by taking into account a combination of commutator rules and Einstein’s sum rule for repeated indices. Therefore, it is an excellent model to test the current status of Computer Algebra Systems (CAS) concerning this kind of quantum-and-tensor-algebra computations and to showcase the CAS technique. The presentation also shows two alternative patterns of steps that can be used for systematically tackling more complicated symbolic problems of this kind.https://www.maplesoft.com/applications/view.aspx?SID=154764&ref=FeedMon, 17 May 2021 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabDigitizing mathematics: ODEs, Special Functions and Solutions to Einstein's Equations
https://www.maplesoft.com/applications/view.aspx?SID=154174&ref=Feed
The material below was presented in the <A HREF="https://www.fields.utoronto.ca/programs/scientific/15-16/semantic/">Semantic Representation of Mathematical Knowledge Workshop</A>, February 3-5, 2016 at the Fields Institute, University of Toronto. It shows the approach used for “digitizing mathematical knowledge" regarding Differential Equations, Special Functions and Solutions to Einstein's equations. While for these areas using databases of information helps (for example textbooks frequently contain these sort of databases), these are areas that, at the same time, are very suitable for using algorithmic mathematical approaches, that result in much richer mathematics than what can be hard-coded into a database. The material also focuses on an interesting cherry-picked collection of Maple functionality, that I think is beautiful, not well know, and seldom focused inter-related as here.<BR><BR>
This application is also featured in a <A HREF="http://www.mapleprimes.com/posts/206715-Digitizing-Mathematics-ODEs-Special">MaplePrimes blog post</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Digitizing mathematics: ODEs, Special Functions and Solutions to Einstein's Equations" style="max-width: 25%;" align="left"/>The material below was presented in the <A HREF="https://www.fields.utoronto.ca/programs/scientific/15-16/semantic/">Semantic Representation of Mathematical Knowledge Workshop</A>, February 3-5, 2016 at the Fields Institute, University of Toronto. It shows the approach used for “digitizing mathematical knowledge" regarding Differential Equations, Special Functions and Solutions to Einstein's equations. While for these areas using databases of information helps (for example textbooks frequently contain these sort of databases), these are areas that, at the same time, are very suitable for using algorithmic mathematical approaches, that result in much richer mathematics than what can be hard-coded into a database. The material also focuses on an interesting cherry-picked collection of Maple functionality, that I think is beautiful, not well know, and seldom focused inter-related as here.<BR><BR>
This application is also featured in a <A HREF="http://www.mapleprimes.com/posts/206715-Digitizing-Mathematics-ODEs-Special">MaplePrimes blog post</A>.https://www.maplesoft.com/applications/view.aspx?SID=154174&ref=FeedFri, 07 Oct 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabNew developments on exact solutions for PDEs with Boundary Conditions
https://www.maplesoft.com/applications/view.aspx?SID=154169&ref=Feed
A collection of two presentations that discuss and illustrate newly implemented methods for computing exact solutions to Partial Differential Equations subject to Boundary conditions.<BR><BR>
These applications are also discussed in two MaplePrimes blog posts:
<UL>
<LI><A HREF="http://www.mapleprimes.com/posts/204436-New-Developments-On-Exact-Solutions">New developments on exact solutions for PDEs with Boundary Conditions</A>
<LI><A HREF="http://www.mapleprimes.com/posts/201226-PDEs-And-Boundary-Conditions--New-Developments">PDEs and Boundary Conditions - new developments</A>
</UL><img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="New developments on exact solutions for PDEs with Boundary Conditions" style="max-width: 25%;" align="left"/>A collection of two presentations that discuss and illustrate newly implemented methods for computing exact solutions to Partial Differential Equations subject to Boundary conditions.<BR><BR>
These applications are also discussed in two MaplePrimes blog posts:
<UL>
<LI><A HREF="http://www.mapleprimes.com/posts/204436-New-Developments-On-Exact-Solutions">New developments on exact solutions for PDEs with Boundary Conditions</A>
<LI><A HREF="http://www.mapleprimes.com/posts/201226-PDEs-And-Boundary-Conditions--New-Developments">PDEs and Boundary Conditions - new developments</A>
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154169&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabQuantization of the Lorentz Force
https://www.maplesoft.com/applications/view.aspx?SID=154168&ref=Feed
Departing from the Hamiltonian of a quantum, non-relativistic, particle with mass m and charge q, evolving under the action of an arbitrary time-independent matgnetic field, derive the expression of the quantized Lorentz force.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/206511-Quantization-Of-The-Lorentz-Force">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/view.aspx?si=154168/quantum.jpg" alt="Quantization of the Lorentz Force" style="max-width: 25%;" align="left"/>Departing from the Hamiltonian of a quantum, non-relativistic, particle with mass m and charge q, evolving under the action of an arbitrary time-independent matgnetic field, derive the expression of the quantized Lorentz force.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/206511-Quantization-Of-The-Lorentz-Force">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154168&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabNth order derivatives and Faa di Bruno formula
https://www.maplesoft.com/applications/view.aspx?SID=154167&ref=Feed
New formulas for symbolic order differentiation and the first ever implementation in computer algebra of the formula by Faa di Bruno for the symbolic order differentiation of composite functions are presented.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/201214-Nth-Order-Derivatives-And-Faa-Di-Bruno-Formula">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Nth order derivatives and Faa di Bruno formula" style="max-width: 25%;" align="left"/>New formulas for symbolic order differentiation and the first ever implementation in computer algebra of the formula by Faa di Bruno for the symbolic order differentiation of composite functions are presented.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/201214-Nth-Order-Derivatives-And-Faa-Di-Bruno-Formula">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154167&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabFactorizing with non-commutative variables
https://www.maplesoft.com/applications/view.aspx?SID=154166&ref=Feed
New capabilities for factorizing expressions involving noncommutative variables are presented and illustrated with a set of examples.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/201368-New-Factorizing-With-Noncommutative-Variables">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Factorizing with non-commutative variables" style="max-width: 25%;" align="left"/>New capabilities for factorizing expressions involving noncommutative variables are presented and illustrated with a set of examples.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/201368-New-Factorizing-With-Noncommutative-Variables">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154166&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabODEs, PDE solutions: when are they "general"?
https://www.maplesoft.com/applications/view.aspx?SID=154165&ref=Feed
This presentation discusses the concept of “general solution” of a Partial Differential Equation, or a system of them, possibly including ODEs and/or algebraic equations, and shows how to tell whether a solution returned by Maple’s <A HREF="/support/help/Maple/view.aspx?path=pdsolve">pdsolve</A> is or not a general (as opposed to particular) solution.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/204437-PDE-Solutions-When-Are-They-general">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="ODEs, PDE solutions: when are they "general"?" style="max-width: 25%;" align="left"/>This presentation discusses the concept of “general solution” of a Partial Differential Equation, or a system of them, possibly including ODEs and/or algebraic equations, and shows how to tell whether a solution returned by Maple’s <A HREF="/support/help/Maple/view.aspx?path=pdsolve">pdsolve</A> is or not a general (as opposed to particular) solution.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/204437-PDE-Solutions-When-Are-They-general">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154165&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabODEs, PDEs and Special Functions
https://www.maplesoft.com/applications/view.aspx?SID=154164&ref=Feed
This presentation illustrates the Maple capabilities for studying and solving ODEs and PDEs, implemented within the <A HREF="/support/help/Maple/view.aspx?path=DEtools">DEtools</A> and <A HREF="/support/help/Maple/view.aspx?path=PDEtools">PDEtools</A> packages, as well as getting information about and working with Special functions of the mathematical language, implemented within the <A HREF="/support/help/Maple/view.aspx?path=FunctionAdvisor">FunctionAdvisor</A>, the conversion network for mathematical functions and the <A HREF="/support/help/Maple/view.aspx?path=MathematicalFunctions">MathematicalFunctions</A> package.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/149877-ODEs-PDEs-And-Special-Functions">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="ODEs, PDEs and Special Functions" style="max-width: 25%;" align="left"/>This presentation illustrates the Maple capabilities for studying and solving ODEs and PDEs, implemented within the <A HREF="/support/help/Maple/view.aspx?path=DEtools">DEtools</A> and <A HREF="/support/help/Maple/view.aspx?path=PDEtools">PDEtools</A> packages, as well as getting information about and working with Special functions of the mathematical language, implemented within the <A HREF="/support/help/Maple/view.aspx?path=FunctionAdvisor">FunctionAdvisor</A>, the conversion network for mathematical functions and the <A HREF="/support/help/Maple/view.aspx?path=MathematicalFunctions">MathematicalFunctions</A> package.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/149877-ODEs-PDEs-And-Special-Functions">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154164&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabGeneral Relativity using Computer Algebra
https://www.maplesoft.com/applications/view.aspx?SID=154163&ref=Feed
This presentation illustrates the use of the functionality of the Physics package for General Relativity in tackling part of the computations of a paper in General Relativity from 2013, mainly about computing a complicated tensorial expression, calculating its trace, then the related traceless expression and finally an exact solution to the corresponding system of nonlinear differential equations.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200192-General-Relativity-Using-Computer-Algebra">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/view.aspx?si=154163/theoreticalphysics.jpg" alt="General Relativity using Computer Algebra" style="max-width: 25%;" align="left"/>This presentation illustrates the use of the functionality of the Physics package for General Relativity in tackling part of the computations of a paper in General Relativity from 2013, mainly about computing a complicated tensorial expression, calculating its trace, then the related traceless expression and finally an exact solution to the corresponding system of nonlinear differential equations.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200192-General-Relativity-Using-Computer-Algebra">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154163&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabMathematicalFunctions:-Sequences
https://www.maplesoft.com/applications/view.aspx?SID=154162&ref=Feed
In this presentation, the <A HREF="/support/help/Maple/view.aspx?path=MathematicalFunctions/Sequences/Nops">MathematicalFunctions:-Sequences package</A>, to add, multiply, differentiate, or map operations over the elements of symbolic sequences (i.e. sequences where the number of elements of the sequence is not known, just represented by a symbol), is presented.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/201103-MathematicalFunctionsSequences">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="MathematicalFunctions:-Sequences" style="max-width: 25%;" align="left"/>In this presentation, the <A HREF="/support/help/Maple/view.aspx?path=MathematicalFunctions/Sequences/Nops">MathematicalFunctions:-Sequences package</A>, to add, multiply, differentiate, or map operations over the elements of symbolic sequences (i.e. sequences where the number of elements of the sequence is not known, just represented by a symbol), is presented.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/201103-MathematicalFunctionsSequences">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154162&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabExact solutions to Einstein's equations
https://www.maplesoft.com/applications/view.aspx?SID=154161&ref=Feed
The Maple database of solutions to Einstein’s equations, constructed digitizing the solutions found in the book “Exact Solutions of Einstein's Field Equations” by Stephani et al. is presented.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/201548-Exact-Solutions-To-Einsteins-Equations">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/view.aspx?si=154161/Einstein.jpg" alt="Exact solutions to Einstein's equations" style="max-width: 25%;" align="left"/>The Maple database of solutions to Einstein’s equations, constructed digitizing the solutions found in the book “Exact Solutions of Einstein's Field Equations” by Stephani et al. is presented.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/201548-Exact-Solutions-To-Einsteins-Equations">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154161&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabTetrads and Weyl scalars in canonical form
https://www.maplesoft.com/applications/view.aspx?SID=154160&ref=Feed
This presentation is about the computation of a canonical form of a tetrad, so that, generally speaking (skipping a technical description) the Weyl scalars are fixed as much as possible (either equal to 0 or to 1) regarding transformations that leave invariant the tetrad metric in a tetrad system of references. Bringing a tetrad in canonical form is a relevant step in the tackling of the equivalence problem between two spacetime metrics (solutions to Einstein's equations).<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/203425-Tetrads-And-Weyl-Scalars-In-Canonical-Form">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/view.aspx?si=154160/theoreticalphysics.jpg" alt="Tetrads and Weyl scalars in canonical form" style="max-width: 25%;" align="left"/>This presentation is about the computation of a canonical form of a tetrad, so that, generally speaking (skipping a technical description) the Weyl scalars are fixed as much as possible (either equal to 0 or to 1) regarding transformations that leave invariant the tetrad metric in a tetrad system of references. Bringing a tetrad in canonical form is a relevant step in the tackling of the equivalence problem between two spacetime metrics (solutions to Einstein's equations).<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/203425-Tetrads-And-Weyl-Scalars-In-Canonical-Form">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154160&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabEquivalence problem in General Relativity
https://www.maplesoft.com/applications/view.aspx?SID=154159&ref=Feed
In this presentation, the equivalence problem for Schwarzschild metric in a simple case is formulated and solved to the end using the <A HREF="/support/help/Maple/view.aspx?path=PDEtools">PDEtools</A>, <A HREF="/support/help/Maple/view.aspx?path=physics">Physics</A> and <A HREF="/support/help/maple/view.aspx?path=Physics/Tetrads">Physics:-Tetrads</A> Maple packages.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/203426-Equivalence-Problem-In-General-Relativity">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/view.aspx?si=154159/quantum.jpg" alt="Equivalence problem in General Relativity" style="max-width: 25%;" align="left"/>In this presentation, the equivalence problem for Schwarzschild metric in a simple case is formulated and solved to the end using the <A HREF="/support/help/Maple/view.aspx?path=PDEtools">PDEtools</A>, <A HREF="/support/help/Maple/view.aspx?path=physics">Physics</A> and <A HREF="/support/help/maple/view.aspx?path=Physics/Tetrads">Physics:-Tetrads</A> Maple packages.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/203426-Equivalence-Problem-In-General-Relativity">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154159&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabMini-Course: Computer Algebra for Physicists
https://www.maplesoft.com/applications/view.aspx?SID=154158&ref=Feed
This is a course, organized as a guided experience, 2 hours per day during five days, on learning the basics of the Maple language, and on using it to formulate algebraic computations we do in physics with paper and pencil. It is oriented to people not familiar with computer algebra (sections 1-5), as well as to people who are familiar but want to learn more about how to use it in Physics.<img src="https://www.maplesoft.com/view.aspx?si=154158/physicscourse.PNG" alt="Mini-Course: Computer Algebra for Physicists" style="max-width: 25%;" align="left"/>This is a course, organized as a guided experience, 2 hours per day during five days, on learning the basics of the Maple language, and on using it to formulate algebraic computations we do in physics with paper and pencil. It is oriented to people not familiar with computer algebra (sections 1-5), as well as to people who are familiar but want to learn more about how to use it in Physics.https://www.maplesoft.com/applications/view.aspx?SID=154158&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabComputer Algebra in Theoretical Physics (IOP Webinar)
https://www.maplesoft.com/applications/view.aspx?SID=154157&ref=Feed
Recent advancements in computational physics are illustrated, showing how these techniques can be applied to problems from general relativity, classical mechanics, quantum mechanics, and classical field theory, including the presentation of the digitization of the solutions to Einstein’s field equations shown in the book “Exact Solutions to Einstein’s Field Equations”.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/203574-Computer-Algebra-In-Theoretical-Physics">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/view.aspx?si=154157/theoreticalphysics.jpg" alt="Computer Algebra in Theoretical Physics (IOP Webinar)" style="max-width: 25%;" align="left"/>Recent advancements in computational physics are illustrated, showing how these techniques can be applied to problems from general relativity, classical mechanics, quantum mechanics, and classical field theory, including the presentation of the digitization of the solutions to Einstein’s field equations shown in the book “Exact Solutions to Einstein’s Field Equations”.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/203574-Computer-Algebra-In-Theoretical-Physics">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154157&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabGround state of a quantum system of identical boson particles
https://www.maplesoft.com/applications/view.aspx?SID=154156&ref=Feed
Departing from the Energy of a quantum system of identical boson particles, the field equation, that is the Gross-Pitaevskii equation, is derived.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200109-Quantum-Mechanics-Using-Computer-Algebra">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/view.aspx?si=154156/quantum.jpg" alt="Ground state of a quantum system of identical boson particles" style="max-width: 25%;" align="left"/>Departing from the Energy of a quantum system of identical boson particles, the field equation, that is the Gross-Pitaevskii equation, is derived.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200109-Quantum-Mechanics-Using-Computer-Algebra">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154156&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabThe Gross-Pitaevskii equation and Bogoliubov spectrum
https://www.maplesoft.com/applications/view.aspx?SID=154155&ref=Feed
The spectrum of its solutions of the equation for a quantum system of identical particles, that is the Gross-Pitaevskii equation (GPE) is derived.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200120-Quantum-Mechanics-II">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/view.aspx?si=154155/theoreticalphysics.jpg" alt="The Gross-Pitaevskii equation and Bogoliubov spectrum" style="max-width: 25%;" align="left"/>The spectrum of its solutions of the equation for a quantum system of identical particles, that is the Gross-Pitaevskii equation (GPE) is derived.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200120-Quantum-Mechanics-II">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154155&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabThe Landau criterion for Superfluidity
https://www.maplesoft.com/applications/view.aspx?SID=154154&ref=Feed
The conditions for superfluidity of a system of identical particles at low temperature are derived.<BR><BR>This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200240-Superfluidity-In-Quantum-Mechanics">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/view.aspx?si=154154/quantummechanics.jpg" alt="The Landau criterion for Superfluidity" style="max-width: 25%;" align="left"/>The conditions for superfluidity of a system of identical particles at low temperature are derived.<BR><BR>This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/200240-Superfluidity-In-Quantum-Mechanics">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154154&ref=FeedThu, 29 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabQuantum Mechanics: Schrödinger vs Heisenberg picture
https://www.maplesoft.com/applications/view.aspx?SID=154153&ref=Feed
Departing from the Shrodinger picture of Quantum Mechanics, the Heisenberg picture and related formulas are derived.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/205867-Quantum-Mechanics-Schrdinger-Vs-Heisenberg">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/view.aspx?si=154153/theoreticalphysicsThumb.jpg" alt="Quantum Mechanics: Schrödinger vs Heisenberg picture" style="max-width: 25%;" align="left"/>Departing from the Shrodinger picture of Quantum Mechanics, the Heisenberg picture and related formulas are derived.
<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/205867-Quantum-Mechanics-Schrdinger-Vs-Heisenberg">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154153&ref=FeedThu, 29 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-Terrab