## Common logical pitfalls when learning to write mathematical proofs

Mathematics is needed in many scientific disciplines, even though it’s used in somewhat different ways in them. A theoretical physicist

Skip to content
## Common logical pitfalls when learning to write mathematical proofs

## Numerical solution of PDE:s, Part 7: 2D Schrödinger equation

## Numerical solution of PDE:s, Part 6: Adiabatic approximation for quantum dynamics

## Numerical solution of PDE:s, Part 5: Schrödinger equation in imaginary time

## Numerical solution of PDE:s, Part 4: Schrödinger equation

## About the NASA’s TRAPPIST-1 findings

## Numerical solution of PDE:s, Part 3: 2D diffusion problem

## Why does quantum mechanics need an infinite dimensional vector space?

## A continuity curiosity

## Numerical solution of PDE:s, Part 2: Implicit method

Mathematics is needed in many scientific disciplines, even though it’s used in somewhat different ways in them. A theoretical physicist

Haven’t been posting for a while, but here’s something new… Earlier I showed how to solve the 1D Schrödinger equation

Having solved the time-dependent Schrödinger equation both in real and imaginary time, we can move forward to investigate systems where

In the last post, I mentioned that the solution of the time dependent 1D Schrödinger equation can be written by

In the earlier posts, I showed how to numerically solve a 1D or 2D diffusion or heat conduction problem using

Yesterday, I was excitedly following the NASA press conference about the exoplanets found orbiting the star TRAPPIST-1 located 39 light

In the earlier posts related to PDE numerical integration, I showed how to discretize 1-dimensional diffusion or heat conduction equations

The infinite-dimensionality of quantum state spaces makes learning QM difficult for many. Here I’ll give a simple example why the fundamental position-momentum commutation relation is not possible with NxN square matrix operators.

It’s sunday, and I don’t feel like writing lots of source code and posting it here today, so I’ll make

In the previous blog post, I showed how to solve the diffusion equation using the explicit method, where the equation