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*It seems they’re still teaching the outdated idea that light is sometimes a wave and sometimes a particle but never both at once. Here’s how the second-quantised electromagnetic field gets rid of this outdated idea.*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

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