List: Road to Quantum Mechanics | Curated by Joseph Mellor

Jul 13, 2024
22 stories
20 saves
Road to Quantum Mechanics
In
Cantor’s Paradise
by
Joseph Mellor
The Road to Quantum Mechanics, Part 1: Intro, Coordinates, and KinematicsIt’s a long road to understanding Quantum Mechanics, and there are no shortcuts. In this series, I’ll show you Quantum Mechanics from the…
Dec 30, 2021
13
Dec 30, 2021
13
In
Cantor’s Paradise
by
Joseph Mellor
Kepler’s Laws and Newtonian MechanicsWe’ll not only explain Newtonian Mechanics, but also derive Kepler’s Laws. This article will serve as an introduction to what doing…
Jan 6, 2022
3
Jan 6, 2022
3
In
Cantor’s Paradise
by
Joseph Mellor
How to Use PDEs to Model RealityOur world isn’t one-dimensional and neither are the partial differential equations that describe it. Let’s talk about how we derive them.
Jan 17, 2022
2
Jan 17, 2022
2
In
Cantor’s Paradise
by
Joseph Mellor
Eigenvalue Equations and PDEsNow that we know how to set up Partial Differential Equations, let’s look at how we can solve them.
Feb 4, 2022
1
Feb 4, 2022
1
In
Cantor’s Paradise
by
Joseph Mellor
The Spherical HarmonicsThe Spherical Harmonics are fundamental to Quantum Mechanics. Let’s derive them.
Feb 14, 2022
1
Feb 14, 2022
1
In
Cantor’s Paradise
by
Joseph Mellor
Bra-Ket Notation and OrthogonalityWe’re going to explain several types of operators fundamental to Quantum Mechanics along with the bra-ket notation.
Mar 1, 2022
1
Mar 1, 2022
1
In
Cantor’s Paradise
by
Joseph Mellor
The Dirac Delta FunctionThe Dirac delta function allows us to model a point source or impulse. Green’s Functions give the response.
Mar 22, 2022
Mar 22, 2022
In
Cantor’s Paradise
by
Joseph Mellor
The Wave EquationWe’re at the end of the PDE arc. Let’s use the techniques we’ve learned to derive, solve, and analyze the Wave Equation.
Apr 10, 2022
3
Apr 10, 2022
3
In
Cantor’s Paradise
by
Joseph Mellor
An Intro to Differential GeometryDifferential Geometry is the study of Calculus on smooth manifolds. It allows you to make statements that are true in any coordinate…
May 12, 2022
4
May 12, 2022
4
In
Cantor’s Paradise
by
Joseph Mellor
Lagrangian MechanicsLagrangian Mechanics makes finding the equations of motion almost trivial and will serve as the basis for modern Physics.
May 27, 2022
1
May 27, 2022
1
In
Cantor’s Paradise
by
Joseph Mellor
The Principle of Least ActionLagrangian Mechanics is more than a shortcut — it’s the basis of modern Physics. Let’s see why that is.
Aug 3, 2022
1
Aug 3, 2022
1
Joseph Mellor
The Classical Double-Slit ExperimentIf you want to figure out whether something is a wave or a particle, you look for interference.
Sep 11, 2022
Sep 11, 2022
In
Cantor’s Paradise
by
Joseph Mellor
The Charged Particle LagrangianEverything in Physics can be represented with a Lagrangian, including particles governed by Maxwell’s Equations and the Lorentz Force Law.
Oct 21, 2022
2
Oct 21, 2022
2
Joseph Mellor
Vectors and CovectorsCovectors are dual to vectors, and they’re fundamental to differential forms and tensors.
Dec 26, 2022
3
Dec 26, 2022
3
Joseph Mellor
An Intro to Differential FormsDifferential forms are powerful tools, but a lot of the geometric intuition is hidden behind the formalism. Let’s fix that.
Jan 25, 2023
2
Jan 25, 2023
2
Joseph Mellor
The Exterior DerivativeWe’re going to derive half the identities in Vector Calculus by introducing a powerful new operator.
Mar 10, 2023
1
Mar 10, 2023
1
Joseph Mellor
k-Chains and k-CellsTo prove the Generalized Stokes’ Theorem, we’ll some way of defining a region and its boundary.
Apr 1, 2023
Apr 1, 2023
Joseph Mellor
An Intro to ManifoldsEuclidean space is the natural environment for Calculus, but manifolds allow us to extend Calculus to curved spaces.
Apr 11, 2023
2
Apr 11, 2023
2
Joseph Mellor
The Generalized Stokes’ TheoremIf there were one theorem to rule them all, it would be the Generalized Stokes’ Theorem.
May 16, 2023
3
May 16, 2023
3
Joseph Mellor
A Mathematical Approach to TensorsA matrix is a linear map of a vector to another vector. A tensor is a multilinear map of a tensor to another tensor.
Jun 4, 2023
2
Jun 4, 2023
2