Author Archives: Mateusz Kwaśnicki

The Dirac equation (3): heuristic derivation

In Section 3 we introduced the Klein-Gordon 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

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Numerical computation of the distribution of the supremum functional

Let be a Lévy process with Lévy-Khintchin 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

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π/2 conjecture solved

A few posts ago I stated the pi-over-two 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

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The Dirac equation (2): heuristic derivation and basic properties of the Klein-Gordon 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

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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 two-year position. The institute is located in the heart of Szczytnicki Park, one of the largest … Continue reading

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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

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Mathematica and hypergeometric functions

Recently I did some numerical experiments in Mathematica involving the hypergeometric function . The results were clearly wrong (a positive-definite matrix having negative eigenvalues, for example), so I spent a couple of hours checking the code. Finally, I discovered a … Continue reading

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