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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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 […]