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My background

Andrius Kulikauskas: I'll be writing here about my background in various subjects.

What do I know of quantum physics?

I have a sense of the basics. I studied four quarters of quantum mechanics in 1985-1986 as a Bachelor student at the University of Chicago. In the first two quarters, we read from Stephen Gasiorowicz's "Quantum Physics", and then we had a quarter of solid state physics and a quarter of nuclear physics. The next year, at the University of California at San Diego, I became friends with John Harland. We were both in the Math Department but he was especially passionate about physics. For as long as I have known him, he has been searching for a physically intuitive understanding of the Copenhagen interpretation of quantum mechanics or some alternative. I suppose the issue is by what intuition should the Schroedinger equation hold up to the collapse of the wave function and yet not further? Personally, I never found the collapse of the wave function troubling for I simply understood it as a reasonable boundary between the quantum world of all possibilities and our classical world of a particular actuality. For me, it simply pointed to the fundamental questions for physics: What is a measurement? and How does nature measure itself?

Recently, I made good progress on the measurement question by noting that we can interpret the binomial theorem in two very different ways, symmetric and asymmetric, which can distinguish the outlooks of an observed and an observer. Abstract: Combinatorial Interpretations Which Distinguish Observer and Observed.

In January 2021, John mentioned that he had found a textbook, "Introduction to Quantum Mechanics" by David J. Griffiths, which he wanted to completely master as a necessary step in his independent research in physics. He agreed that I study along with him and suggested that we talk for an hour every other week. My own goal is to understand quantum mechanics well enough to help me better intuit Lie groups and related mathematics which arises in my philosophy. Also, I want to accumulate and apply knowledge of the ways of figuring things out in physics, and show how those relate to the ways in math and other disciplines.

Griffiths's textbook is oriented around calculation as the main activity of theoretical physics. This made me appreciate that calculation is the way of figuring things out in physics that manifests the duality of math and physics, in that every mathematical term can be understood to have physical meaning.

In catching up with John, and gliding through the initial chapters, I realized that I would have to do some calculations myself in order to absorb anything. Given my background in combinatorics, I thought to inquire what the Hermite polynomials and other such polynomials might mean...