
Recent Posts
Recent Comments
Alexander Perlis on Heronian triangles conjecture Mateusz Kwaśnicki on Mathematica and hypergeometric… juanmarqz on Mathematica and hypergeometric… mateuszkwasnicki on Heronian triangles conjecture Johannes boot on Heronian triangles conjecture Archives
Categories
Meta
Author Archives: Mateusz Kwaśnicki
The Dirac equation (3): heuristic derivation
In Section 3 we introduced the KleinGordon equation (formula (3.2)). Although it is a fundamental equation in relativistic quantum mechanics, it does not really fit the quantum world framework. The wave function does not completely describe the state of a … Continue reading
Posted in Uncategorized
Leave a comment
Numerical computation of the distribution of the supremum functional
Let be a Lévy process with LévyKhintchin exponent for a complete Bernstein function (some examples below). Let be the supremum functional of . Given some growth condition on , a formula for was given in my recent preprint written with … Continue reading
Posted in numerical math
Tagged complete Bernstein function, levy process, Mathematica, Numerical maths, Supremum
Leave a comment
π/2 conjecture solved
A few posts ago I stated the piovertwo concecture. Recently, my friend and collegue Jacek Małecki proved it in full generality. (He did it while I was on my vacation in November — sometimes it is good to take a … Continue reading
Posted in open problems
Tagged Bernstein function, contour integral, pi, representation theorem
Leave a comment
The Dirac equation (2): heuristic derivation and basic properties of the KleinGordon equation
For more than a century now, we know that light presents some properties typical to particles (for example, in the photoelectric effect, explained in 1905 by Albert Einstein), and also matter can behave as waves (which was first conjectured by … Continue reading
Posted in Dirac equation
Tagged Dirac equation, KleinGordon equation, spectral theorem
Leave a comment
Job in a city park
Since October 2010 I work in the Wrocław branch of the Institute of Mathematics of the Polish Academy of Sciences, where I have a twoyear position. The institute is located in the heart of Szczytnicki Park, one of the largest … Continue reading
The Dirac equation (1): introduction
Although it took me much more time than I expected, the introductory part of the notes on the Dirac equation is ready. I welcome all comments. In order to properly understand the Dirac equation, one needs some background on the … Continue reading
Posted in Dirac equation
Tagged Dirac equation, Lorentz transformation, Maxwell's equations, notes, seminar
Leave a comment
Mathematica and hypergeometric functions
Recently I did some numerical experiments in Mathematica involving the hypergeometric function . The results were clearly wrong (a positivedefinite matrix having negative eigenvalues, for example), so I spent a couple of hours checking the code. Finally, I discovered a … Continue reading