The conceptual foundations of Quantum Physics.

A comprehensive A-Z guide that will save you a ton of time in searching elsewhere trying to piece all the different information together.

Quantum Theory without falling into oversimplifications or hyped versions and yet conceived for an audience of non-physicists.

The double silt experiment, the wave particle duality, entanglement, quantum superposition, the uncertainty principle of Heisenberg, SchrÃ¶dinger's cat paradox, quantum tunneling and much more.

A course that fills the gap between a too popularized version of Quantum Mechanics and too high level university courses.

You will learn all the basics, enabling you to distinguish between mere speculative interpretations in fashion and the real experimental facts.

**Note:** Take a look at the free lectures! Scroll down to the curriculum and click on ‘Basics I’. The ‘preview’ lectures are free. That might help you to get a better feeling on what’s about.

**Why this course? **This is an introductory course (Basics) that originates from my desire to share my knowledge of the mysterious and fascinating world of Quantum Physics. Considering how the media (sometimes also physicists) present Quantum Theory focusing only on highly dubious ideas and speculations backed by no evidence or, worse, promote pseudo-scientific hypes that fall regularly into and out of fashion, I felt it necessary to create a serious introduction to the conceptual foundations of Quantum Physics. The second part (Supplemental), which focuses further on some selected topics, can be found on the Udemy portal as well.

**Who is it for?** For the autodidact who is looking for a serious and rigorous introduction to the foundations of quantum physics and some of its philosophical implications. This course does not need a technical background except for some basics, such as elementary concepts of algebra, trigonometry, calculus and statistics. It is easier than a university course but needs more effort than a popular science lecture. It might be easier for those having already some math background but a mathematical appendix is furnished for those who need a reminder.

Even though these lectures are not a replacement for college courses they could complement it. University or college classes do not address the foundations and the philosophical aspects of Quantum Physics, teaching Quantum Mechanics mostly from the formal and mathematical perspective, which is something we will restrict only to the essential basics here. While in schools, colleges and universities, Quantum Physics is taught with a dry and almost exclusively technical approach which furnishes only a superficial insight on its foundations, this course is recommended also to high school, undergraduate and graduate students who would like to look further. Not only physicists could (re-)discover some topics but philosophers, engineers, IT students or historians of science could acquire with this course a basic preparation which is unlikely to be offered in most departments. This online course proposes itself also to become part of a faculty curriculum in departments or other institutions which would like to expand their interests towards the foundations of Quantum Physics (contact the instructor for details).

**What is it about?** A course on the conceptual foundations of Quantum Physics on topics that you won’t find elsewhere explained at introductory level. It will lead you by hand as clearly as possible from the abc of Quantum Mechanics to the most recent experiments and its implications.

We review the standard concepts like the wave-particle duality, Heisenberg`s uncertainty principle, Schrödinger`s cat, the vacuum zero-point energy and virtual particles, among several others. Then we deepen the subject analysing quantum entanglement, the so called “EPR paradox” which question our naive understanding of the meaning of reality and locality (for more details on the content look up the curriculum page).

My aim is to deliver the material necessary so that you will be able by yourself to distinguish between mere speculative (and more or less extravagant) interpretations in fashion, and the real Quantum Theory and its experimental facts as it is.

1

Introduction to the course

Some preliminary comments about the aim, idea, structure and content of the course and how it distinguishes itself from other courses on Quantum Physics.

1

The Nature of Light

Some few historic remarks on how the nature of light was understood from the ancient Greece to Thomas Young's double slit experiment.

2

Fields, Waves and Interference

Introduction to the concept of force field and the interference of waves.

3

Young's Double Slit Experiment

This lecture describes the famous double slit experiment of Thomas Young. It is one of the most classical experiments which suggest the wave-like nature of light and which remains until nowadays the paradigm experiment of Quantum Physics.

4

The Blackbody Radiation before Max Planck

Before 1905, according to classical physics every material object that is not frozen to the absolute zero temperature should emit an infinite amount of energy. Here we describe why inside classical physics this paradox could not find a resolution.

5

The Blackbody Radiation after Max Planck

The historical point of departure of quantum theory was Planck's derivation of the black body radiation which assumed energy to be quantized. Previously it was thought that energy is a continuous phenomenon. Its quantization was a conceptual revolution that can be compared to a sort of "Copernican revolution".

6

Check your understanding (lectures 2-6)

7

Quizzes for lectures 2-6

These are the quizzes relating to lectures 2-6

8

The Photoelectric effect

The photoelectric effect comes as a further validation of the fact that energy appears always quantized. The photoelectric effect was explained by Einstein introducing the notion of the light particle, the "photon".

9

Bohr's atomic model

Bohr, inspired by the result of the photoelectric effect, advances his famous "planetary model" of the atom.

10

The Franck-Hertz experiment

Bohr's atom model seemed to receive experimental validation by Frank-Hertz's experiment which definitely demonstrated that atoms absorb energy in quantized amounts of energy.

11

The Compton effect

The Compton scattering of photons and showed further that electromagnetic radiation has also a corpuscular nature.

12

Pair creation and annihilation

Pair creation and annihilation shows how matter and anti-matter particles can transform in pure energy and back. It is another example that showed that electromagnetic radiation has a corpuscular nature.

13

Check your understanding (lectures 7-11)

14

Quizzes for lectures 7-11

15

Waves strike back: Bragg diffraction and the de Broglie hypothesis

Bragg diffraction and the de Broglie hypothesis pave the way for understanding better the wave-particle duality problem.

16

The wave-particle duality

Are photons and electrons particles or waves? If they are both, when do they show upn as one or the other aspect? The wave-particle duality illustrated by Young's double slit experiment will shed some light on this.

17

The Heisenberg's uncertainty principle

Heisenberg's uncertainty principle is explained and some of its frequent misinterpretations illustrated.

18

Check your understanding (lectures 12-14)

19

Quizzes for lectures 12-14

20

The wavefunction and the measurement problem

The concept of the wavefunction in quantum mechanics is explained. We will address the question if the wavefunction is a mere mathematical object or if it represents a real physical entity.

21

The state vector, observables and the measurement postulate

The description of the quantum world in terms of a probabilistic interpretation led to a mathematical formalism which is quite different than that used in classical physics. Classical states and dynamical variables are replaced by state vectors and operators, the "observables". The measurement postulate captures the essence of how a measurement is represented in QM.

22

The SchrÃ¶dinger's equation

SchrÃ¶dinger's equation and the time evolution operator are the formal base for a successful understanding of atomic physics.

23

Atomic orbitals

The modern concept of the structure of atoms in quantum mechanical terms relies on a probabilistic description. Electrons around the atomic nucleus have no longer defined positions or orbits but must be described by probability distributions, the atomic orbitals.

24

Check your understanding (lectures 15-18)

25

Quizzes for lectures 15-18

1

Angular momentum in classical physics

A short introduction to angular momentum in classical physics.

2

Spin: do particles rotate?

Angular momentum and spin are physical quantities which we intuitively ascribe to rotating objects. Do they apply in the same way for elementary point particles?

3

Commutation relations and quantum algebra

The Stern-Gerlach experiments were decisive in demonstrating the impossibility to know the particles's spin values along two directions at the same time and laid the foundations for a new quantum algebra.

4

Check your understanding (lectures 19-21)

5

Quizzes for lectures 19-21

6

Is information fundamental?

In quantum mechanics the abstract notion of "information" seems to be a much more concrete and 'real' thing as we might have expected. This reveals us also how quantum physics is contextual, that is, the answer a quantum particle or system delivers us in a measurement depends from the context we perform it.

7

The spinning world of spinors

What happens if we measure the spin of a particle along non-orthogonal axes?

8

A weird quantum rotation

Also the concept of rotation can be quite different in quantum physics than in classical physics.

9

The photon's polarization and spin

Hoe does the polarization of a wave relate to the particle-picture of photons in quantum physics? Also photons have spin as electrons, but they have some specific peculiarities which must be pointed out.

10

Check your understanding (lectures 22-25)

11

Quizzes for lectures 22-25

12

Quantum superposition: being in two states at the same time

Can particles spin clockwise AND anti-clockwise at the same time? In the microscopic quantum world it is a normal state of affairs.

13

The Time-Energy uncertainty

In analogy to Heisenberg's uncertainty over position and momentum, likewise it is impossible to determine with absolute precision the energy of a system at a definite time. There are however fundamental differences between the two uncertainties.

14

The tunnel effect: jumping over forbidden barriers

Can a particle jump through a classically forbidden barrier? Quantum mechanics allows to tunnel through a potential barrier even if it has not the classical allowed energy to do that.

15

Vacuum zero-point energy, virtual particles and the Casimir effect

Is "empty" space really empty? According to quantum physics there can't exist no such thing. We will take a look at the vacuum zero-point energy, the concept of virtual particles and the Casimir effect.

16

The Bohr-Einstein Debate

Einstein and Bohr did not agree on how to interpret quantum physics. Einstein tried to disprove it with thought experiments and Bohr pointed out its fallacies. The Copenhagen interpretation of quantum mechanics took shape.

17

Check your understanding (lectures 26-30)

18

Quizzes for lectures 26-30

19

Quantum indistinguishability

Two identical elementary particles are no longer distinguishable after interaction. They will form a unique indistinguishable whole.

20

Quantum entanglement

In quantum theory particles can be entangled with each other also light years away and apparently "feel" instantly the state of the other. How should this be correctly interpreted?

21

The EPR paradox (original version)

A. Einstein, B. Podolsky and N. Rosen proposed a thought experiment that was supposed to show how it is possible to circumvent the commutation relations of QM and why it has to be considered therefore an incomplete theory. Were they right?

22

The EPR paradox (modern form)

The EPR paradox is obtained with the spin observables, as it is usually illustrated in modern textbooks.

23

Faster than light transmission?

Some quantum phenomena seem to imply an action at a distance faster than light. Instant correlation between particles also light years apart are possible. Does this allow for faster than light transmission of information?

24

SchrÃ¶dinger`s cat: ``dead or aliveÂ´Â´, or Â´Â´dead and aliveÂ´Â´?

Can a cat be dead AND alive at the same time? Quantum mechanics seems to suggest this, however at a closer inspection the paradox is tricky.

25

Quantum decoherence and the measurement problem

Quantum decoherence solves only partially the SchrÃ¶dinger's cat paradox. The measurement problem still defeats a final resolution.

26

Check your understanding (lectures 31-37)

27

Quizzes for lectures 31-37

28

Extra lecture: Quantum physics from the perspective of philosophical idealism

This is a standalone lecture of quantum physics from a purely philosophical perspective. Philosophical idealism gives us an insight into reality which reveals how not only our senses but also our mind deceives us in seeing reality and could be potentially useful to keep in mind when we ponder about the ontology of the quantum world.

1

Final considerations and outlook

1

Appendix - Part I : Elementary mathematical introduction

The first notions of elementary algebra, Pythagorean theorem, the Cartesian coordinate system, and the parallelogram law of vector addition.

2

Appendix - Part II : waves and complex numbers

A brief introduction on how functions can describe waves and its representation with complex numbers and complex functions.

3

Appendix - Part III : more on waves and some calculus

How waves are added and the interference term appears, the notion of the derivative and differential and an elementary intuitive explanation of integration.

4

Linear momentum and kinetic energy

Momentum must be carefully be distinguished from kinetic energy!

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Definitely! If you have an internet connection, courses on Udemy are available on any device at any time. If you don't have an internet connection, some instructors also let their students download course lectures. That's up to the instructor though, so make sure you get on their good side!

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