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Quantum mechanics

Quantum mechanics (hence, QM) is humanity’s most astounding achievement in understanding how our universe works. It completely upends our ordinary understanding of matter, time, and space, yet does so in a way that is mathematically rigorous and testable.

Many high school physics classes have a week or two week long sequence on QM. This is often done in Honors or AP Physics, or perhaps in a science elective. This could even be done in regular college-prep level physics classes, if students are so motivated.

Here I have compiled my resources on teaching QM. These were developed separately so there is some overlap, which will be addressed over time.

There is no mathematics required to cover this sequence. However, it requires that students already have mastered an understanding of

basic ideas of classical physics: kinematics, energy, and momentum

superposition of waves

constructive and destructive interference of waves

classical models of the atom

This is only a brief introductions to QM. I can’t stress enough how important it is to read more for a fuller understanding of this topic. See the list of recommended books at the end of this page.


The laws of classical physics appear true – i.e., the equations work! They work for any object larger than a speck of dust, under almost all imaginable conditions. Yet some phenomenon simply can’t be explained by classical physics.  We kept discovering new phenomenon, under certain circumstances, that “broke all the rules” of classical mechanics.  That’s when we were led to develop QM (Quantum mechanics.)

The rules at first appeared bizarre.  Most everything we think of as a particle, now was revealed to have wave-like characteristics. Deterministic cause-and-effect was replaced by a very special kind of statistical randomness.  Particles like electrons could even appear to disappear from the universe at one point and reappear at a different point –  a quantum leap.

Yet everything we already know about the everyday world is still true. Cars, asteroids, and joggers don’t have quantum leaps.  People, apples, and dogs don’t have any visible wave-properties. Cause-and-effect works.

This sounds like we have two completely different set of rules for our universe. How can either set of rules be true when they contradict each other?

Answer: instead of classical physics contradicting QM, we have learned that classical physics emerges from QM. When you add together the weird quantum behavior of many particles, they ‘average out’ to create the ‘normal’ behavior that we see in our everyday world.

So we don’t throw away classical physics – it really does work for most objects, in most cases. Using classical physics to analyze the path of a baseball or electricity in a circuit is billions of time simpler than starting from scratch at a QM level.

When one set of rules “emerges” from what appears to be a very different set of rules, we have an example of Emergent phenomenon


The nature of reality itself! The allegory of the cave

The wave nature of matter

Why did we have to develop modern physics? What is wrong with just keeping classical physics?

Early quantum theory

Schrodinger model of the atom

How does the Schrodinger equation create orbitals?

Heisenberg Uncertainty Principle

Schrodingers cat

What does the wave function actually mean?

The consequences of quantum mechanics

What are covalent bonds between atoms?

The normal force: So, objects really never touch?

How time and space could be a quantum error correcting code

The origins of space and time

Quantum teleportation (and it isn’t what you think)

Time’s arrow may be traced to quantum source

The quantum thermodynamics revolution

The four possible types of multiverses

Parallel universes in quantum mechanics

Recommended books

I suggest these books. If one puts in the effort then one comes out with a better understanding of the subject.

The Cosmic Code: Quantum Physics as the Language of Nature, Heinz R. Pagels

The Cosmic Code

Quantum Reality: Beyond the New Physics, Nick Herbert

Quantum Reality Nick Herbert

In Search of Schrödinger’s Cat: Quantum Physics and Reality, John Gribbon

John Gribbon

Learning Standards

SAT Subject Test: Physics

Quantum phenomena, such as photons and photoelectric effect
Atomic, such as the Rutherford and Bohr models, atomic energy levels, and atomic spectra
Nuclear and particle physics, such as radioactivity, nuclear reactions, and fundamental particles
Relativity, such as time dilation, length contraction, and mass-energy equivalence

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)

Electromagnetic radiation can be modeled as a wave of changing electric and magnetic fields or as particles called photons. The wave model is useful for explaining many features of electromagnetic radiation, and the particle model explains other features. Quantum theory relates the two models…. Knowledge of quantum physics enabled the development of semiconductors, computer chips, and lasers, all of which are now essential components of modern imaging, communications, and information technologies.

Massachusetts Science and Technology/Engineering Curriculum Framework 2006

Chemistry: Atomic Structure and Nuclear Chemistry
Atomic models are used to explain atoms and help us understand the interaction of elements and compounds observed on a macroscopic scale. Nuclear chemistry deals with radioactivity, nuclear processes, and nuclear properties. Nuclear reactions produce tremendous amounts of energy and lead to the formation of elements.

2.1 Recognize discoveries from Dalton (atomic theory), Thomson (the electron), Rutherford (the nucleus), and Bohr (planetary model of atom), and understand how each discovery leads to modern theory.
2.2 Describe Rutherford’s “gold foil” experiment that led to the discovery of the nuclear atom. Identify the major components (protons, neutrons, and electrons) of the nuclear atom and explain how they interact.
2.3 Interpret and apply the laws of conservation of mass, constant composition (definite proportions), and multiple proportions.
2.4 Write the electron configurations for the first twenty elements of the periodic table.
2.5 Identify the three main types of radioactive decay (alpha, beta, and gamma) and compare their properties (composition, mass, charge, and penetrating power).
2.6 Describe the process of radioactive decay by using nuclear equations, and explain the concept of half-life for an isotope (for example, C-14 is a powerful tool in determining the age of objects).
2.7 Compare and contrast nuclear fission and nuclear fusion.

AP Physics Curriculum Framework
Essential Knowledge 1.D.1: Objects classically thought of as particles can exhibit properties of waves.
a. This wavelike behavior of particles has been observed, e.g., in a double-slit experiment using elementary particles.
b. The classical models of objects do not describe their wave nature. These models break down when observing objects in small dimensions.

Learning Objective 1.D.1.1:
The student is able to explain why classical mechanics cannot describe all properties of objects by articulating the reasons that classical mechanics must be refined and an alternative explanation developed when classical particles display wave properties.

Essential Knowledge 1.D.2: Certain phenomena classically thought of as waves can exhibit properties of particles.
a. The classical models of waves do not describe the nature of a photon.
b. Momentum and energy of a photon can be related to its frequency and wavelength.

Content Connection: This essential knowledge does not produce a specific learning objective but serves as a foundation for other learning objectives in the course.

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