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Computational Physics Quantum Mechanics

Numerical Quantum Mechanics: The Time-dependent Schrödinger Equation (III)

Back in 2016, I wrote two blog posts (I and II) concerning how to solve the time-dependent Schrödinger equation (TDSE) numerically. Although I gave recipes for computing the spatial derivative that occurs in the TDSE, and for integrating the TDSE itself, I omitted a rather important aspect of the computation: boundary conditions (BC’s). In this […]

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Sci-Fi

The Trisolaran probe from Liu Cixin’s ‘The Three-Body Problem’

A friend recently recommend Liu Cixin’s amazing Three-Body trilogy to me, and I am almost done reading the third book. The second book of the series, The Dark Forest, contained an alien spacecraft that I immediately wanted to visualize. I highly recommend this trilogy, and will try to avoid spoilers as much as possible! The […]

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Music

Oaken Moths – Rings of Saturn (video)

Koen and I have made a new ambient track called ‘Rings of Saturn’. For the first time, we’ve also made an accompanying video, which is constructed out of genuine NASA/ESA footage of Saturn and its moons, taken by the Cassini space probe:

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Sci-Fi

Rendezvous with Rama, v1.0

It’s been far too long – three years! – but it’s finally time for me to finish my depiction of Rama, the spaceship from Arthur C. Clarke’s novel ‘Rendezvous with Rama’. I have done some more work on Rama in 2018, but never posted it, because it was an incremental update. Mostly, I have revised […]

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Music

Music update: Oaken Moths, Procyon, BlackHoleCam

For close to two decades, I have been producing and releasing electronic music. I haven’t always had a great deal of time and energy to put into it – my PhD took a lot of that – but recently, I’ve been producing a bit more again, and I thought I’d share an update via this […]

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Computational Physics Quantum Mechanics

Quantum Mechanics: Ground States for 2 Charged Particles in the 1D Infinite Square Well

In this blog post I want to have a look at the Coulomb interaction, the governing equation of electrostatics, in the context of quantum mechanics. In my undergraduate QM courses, when discussing multi-particle systems, the first thing textbooks tended to do was to turn off the Coulomb interaction to render the problems analytically tractable. The hydrogen […]

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Computational Physics Quantum Mechanics

Numerical Quantum Mechanics: The Time-dependent Schrödinger Equation (II)

In my previous blog post, I had an introductory look at the problem of integrating the time-dependent Schrödinger equation (TDSE) numerically, plotting the wave function at each time step, and creating an animation of the result. In this post I will describe how to solve the TDSE in more detail. Recall the TDSE for a spinless particle in a […]

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Computational Physics Quantum Mechanics

Numerical Quantum Mechanics: The Time-dependent Schrödinger Equation (I)

In quantum mechanics, particles are represented by ‘wave functions’, wavy entities that are extended in space. The square modulus of the wave at any location gives the probability density of finding the particle at that location. The behavior of the waves is given by the time-dependent Schrödinger equation – a wave equation that describes how the waves evolve in time. […]

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Sci-Fi

Rendezvous with Rama

I’ve recently been reading some of the old Sci-Fi masters, and I really fell in love with Arthur C. Clarke’s ‘Rendezvous with Rama’. I’ve read it twice now and was completely engrossed both times – I can’t recommend this book enough! I decided I wanted to recreate the titular spaceship using CGI, and have been working […]