Why Quantum Mechanics?

Chem 3240 · Lecture 1.1

Davit Potoyan

Five things classical physics cannot explain

Why does hot iron glow red, then white?

Why is the sky blue?

Why do stars and neon signs shine in sharp lines?

Why doesn’t the electron crash into the nucleus?

Why do electron clouds come in these shapes, and why does the periodic table follow from them?

Every one of these is answered in this course.

What is quantum mechanics?

The fundamental theory of nature, governing atoms, molecules, and subatomic particles.

  • A complete description of physical reality
  • Has never failed an experimental test since its discovery
  • Verified to an astonishing degree of accuracy

the most precisely tested prediction in all of science: theory and experiment agree to one part in a trillion. Fan, X., Myers, T. G., Sukra, B. A. D., & Gabrielse, G. (2023). Measurement of the electron magnetic moment. Phys. Rev. Lett. 130, 071801. doi:10.1103/PhysRevLett.130.071801

Beware: quantum mechanics is weird 🤯

“I think I can safely say that nobody understands quantum mechanics.”

Richard Feynman

Be prepared to let go of the idea that “things make sense.” We can still master the logic of QM and apply it everywhere.

Zoom in

protein: Newton’s laws, ~10,000 atoms

water molecule: nuclei classical, electrons quantum, computed for this course

one electron in hydrogen: pure quantum, no orbit, only a wave

Same matter, three levels of description. This course is about the right-hand end.

QM is not “just another theory”

In the hierarchy biology → chemistry → physics → math, quantum mechanics sits in a unique spot:

It is like the operating system on which other theories run as “apps.”

Translating a classical theory into this OS is what physicists call quantization.

Scott Aaronson, Quantum Computing Since Democritus (2013)

Chemistry runs on quantum mechanics

One year after the Schrödinger equation, Dirac (1929) declared the game over:

“The underlying physical laws necessary for … the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.”

  • Every bond, reaction barrier, color, and spectrum is a solution of one equation
  • A century of cleverness (plus computers, plus now AI trained on millions of quantum calculations) went into extracting those solutions

What you will compute yourself

a wavepacket tunneling through a wall

quantized states of a trapped particle

standing waves, the template for orbitals

molecular orbitals of benzene, in ten lines of Python

And then quantum mechanics became a technology

“Nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical.”

Richard Feynman (1982)

  • Superposition and entanglement turned out to be resources
  • A qubit is just a two-level quantum system; a quantum computer computes with wavefunctions
  • The killer app: simulating molecules, exactly this course’s subject
  • Everyday hardware already runs on QM: transistors, LEDs, lasers, MRI, the atomic clocks behind GPS

What skills will you gain?

  • Probabilistic thinking and comfort with uncertainty
  • Linear algebra + differential equations, applied for real
  • Ability to decode electronic structure calculations in research papers
  • Insight into bonding, spectroscopy, and reactivity

the molecular orbitals of water: by the end you will read this diagram at a glance, and compute it yourself

Takeaway

Chemistry is applied quantum mechanics. If you feel you don’t fully understand QM, you’re in good company, with everyone else. The goal is to master its logic, not its intuition.