## The problematic radial momentum operator

In quantum mechanics, position coordinates x,y,z of a particle are replaced with position operators and the components of the momentum

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# Category: Quantum Mechanics

## The problematic radial momentum operator

## 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

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

In quantum mechanics, position coordinates x,y,z of a particle are replaced with position operators and the components of the momentum

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

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.