Quantum Mechanics

Contents

How to Derive the Schrödinger Equation

The Meaning of Basic Time Evolution in Quatum Mechanics

A New Approach to the Quantum Harmonic Oscillator

Beginning with only the notion of a quantum system whose observables all vary harmonically with time and the canonical commutation relationship, one can fully derive the wonted Quantum Harmonic Oscillator.

How Can We Interpret Polarisation and Frequency When Dealing With One Photon?

I explain how one photon relates to Maxwell’s equations and the classical theories of light.

Are Coherent States of Light Classical or Quantum?

More on how classical optics is embedded in the larger whole of modern quantum theory.

The Difference Between Quantum Measurements and Properties

A quantum system’s properties and measurements are very different, as explained here.

The Heisenberg Picture of Quantum Mechanics from the Classical Hamiltonian Formalism

How does classical physics “continuously deform” into quantum physics: I explain how classical physics becomes seen to be embedded in the larger whole of modern quantum theory.

Is Light a Wave or a Particle?

It seems they’re still teaching the outdated idea that light is sometimes a wave and sometimes a particle but never both at once. Here’s how the second-quantised electromagnetic field gets rid of this outdated idea.

Divergences in Second-Quantised Field Theories

I explain why infinities in quantum mechanics don’t worry me as much as they used to.

Non-Normalisable States and Rigged Hilbert Space in Quantum Mechanics

On the taming of Dirac Deltas, Infinite Plane Waves and other monsters.

The Heisenberg Uncertainty Principle and Canonical Commutation Relationships in Quantum Mechanics

On the fundamental equivalence of these two concepts

Why are orthogonal functions and eigenvalues/functions so important in quantum mechanics?

I look at why these concepts are central to the mathematics of quantum mechanics

Why Quantum Mechanics is Easy!

Do you find quantum mechanics baffling? Have you ever thought that simply doing everything by “simple” classical statistics and probability theory might be more concrete and easier? Think again!

Mixed Quantum States, Wigner’s Friend and the Mueller and Density Matrices

A mixed quantum state is more complicated than a pure state. Here I illustrate this concept with the Wigner’s Friend thought experiment and show how its analysis is deftly handled by the density matrix approach.

Can Planck’s Constant Be Derived fro Maxwell’s Equations?

Of course not! But Maxwell’s equations and the Lorentz transformation do indeed constrain the Planck Law’s form.

Quantum Jumps Are Really Smooth Slides

The atomic state transitions that give rise to absorption spectrums do not happen instantaneously: Wigner-Weisskopf theory is the description of how this all happens smoothly, albeit fantastically swiftly.