**Introduction to quantum mechanics**

- ★★★★★ From polarisation to quantum mechanics: states, observables, Born's law
- ★★★★★ Projection operators, generalised Born's rule, position basis, wavefunction
- ★★★★★ Dealing with eigenspaces; noncommuting variables and another postulate
- ★★★★★ Position, momentum bases and operators, Fourier transform, uncertainty
- ★★★★☆ Systems and sub-systems, tensor product space, quantum entanglement
- ★★★★☆ Mixed states I: density matrix, partial trace, the most general Born rule
- ★★★★☆ Mixed states II: decoherence; important measures of purity and entropy
- ★★★★☆ Time evolution, Schrodinger and Heisenberg pictures, Noether's theorem
- ħ→0: Emergence of classical phenomena, waves in quantum theory
- Important operators: angular momentum, spin and other related
- Examples
- Open quantum systems
- Interesting no-go theorems
- Symmetries and superselection

**Quantum information/computing/probability/logic**

**Philosophy of quantum mechanics**

- Comments on the axiomatisation of quantum mechanics and theory
- Quantum mechanics as a replacement for probability theory
- Obligatory comment on quantum foundations

Plan for quantum foundations article:

- (copy over the rant from article 1) -- Wigner's friend. Exclusivity of states is a way to reproduce the same results of the "hidden reality" of classical mechanics without having one.
- "Shut up and calculate" because logical positivism
- What exactly is superposition? "Or" not "and" and it talks about our knowledge of the state (our knowledge is probabilistic)
- What exactly makes a theory quantum (commutators/bounds on uncertainty)?
- Superpositions vs mixed states -- they are completely different and unrelated. It doesn't matter the language we use to describe them may be sometimes similar (e.g. "the photon has a 50% probability of being vertically polarised..."), they are mathematically different, and physically different, which means they can be tested empirically (by using a diagonal filter). This is a limitation of language, not of physics.
- Quantum entanglement -- "or" and logical positivism clarify things -- look at stuff from each/any observer's perspective.

Plan for axiomatization article:

- axiomatisation vs motivation -- e.g. Born's law, eigenvalues as observables, etc.
- state axioms, separated into fundamental axioms and one that has to do with our theory
- quantum theory vs a specific quantum theory
- de Broglie stuff -- do we derive momentum from de Broglie or from Noether's theorem? In terms of mathematical axiomatisation and in terms of physical motivation (give the original motivation)
- Gleason's theorem
- Rigged Hilbert spaces

Other stuff: path integrals, variational QM, raising and lowering operators, creation and annihilation operators, ground states, Fock space, entanglement monogomy, Bloch sphere, quantum computing [1], Wigner-Weyl transform, Wigner quasiprobability distribution, quantisation... https://motls.blogspot.com/2011/06/density-matrix-and-its-classical.html

https://en.wikipedia.org/wiki/Purity_(quantum_mechanics)

Decoherence, https://motls.blogspot.com/2014/10/redundant-synonyms-of-decoherence.html

https://motls.blogspot.com/2014/10/redundant-synonyms-of-decoherence.html

https://physics.stackexchange.com/questions/317126/off-diagonal-elements-of-density-matrix-measurement-of-coherence

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no-cloning,

no-communication,

https://en.wikipedia.org/wiki/Quantum_entanglement#Classification_of_entanglement,

https://en.wikipedia.org/wiki/Quantum_entanglement#Entropy

Bell's theorem, enwp.org/Bell_state, motls.blogspot.com/2019/06/bells-inequality-is-straightforward.html, https://motls.blogspot.com/2017/09/why-vanishing-commutators-imply-theres.html

Does Bob create hidden variables for Alice? What does Bell's experiment say here?

---

https://motls.blogspot.com/2011/11/how-classical-fields-particles-emerge.html

Classical approximation -- Ehrneferst, hbar approach zero, decoherence, just looking at probabilities, quantisation

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box, well, tunneling, H atom, double-slit

double-slit weirdness

https://qchu.wordpress.com/2011/07/16/the-heisenberg-picture-of-quantum-mechanics/ -- worked out examples

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The energy-time uncertainty principle

https://motls.blogspot.com/2016/03/measurement-isnt-violation-of-unitarity.html

quora.com/What-is-a-tensor-product-in-quantum-mechanics/answer/Charuhas-Shiveshwarkar

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https://en.wikipedia.org/wiki/Open_quantum_system

https://en.wikipedia.org/wiki/Lindbladian

https://en.wikipedia.org/wiki/Belavkin_equation

https://motls.blogspot.com/2017/02/lindblad-equation-cant-solve-any.html

**Mixed states II**https://en.wikipedia.org/wiki/Purity_(quantum_mechanics)

Decoherence, https://motls.blogspot.com/2014/10/redundant-synonyms-of-decoherence.html

https://motls.blogspot.com/2014/10/redundant-synonyms-of-decoherence.html

https://physics.stackexchange.com/questions/317126/off-diagonal-elements-of-density-matrix-measurement-of-coherence

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**Theorems**no-cloning,

no-communication,

https://en.wikipedia.org/wiki/Quantum_entanglement#Classification_of_entanglement,

https://en.wikipedia.org/wiki/Quantum_entanglement#Entropy

Bell's theorem, enwp.org/Bell_state, motls.blogspot.com/2019/06/bells-inequality-is-straightforward.html, https://motls.blogspot.com/2017/09/why-vanishing-commutators-imply-theres.html

Does Bob create hidden variables for Alice? What does Bell's experiment say here?

---

**Classical limits**https://motls.blogspot.com/2011/11/how-classical-fields-particles-emerge.html

Classical approximation -- Ehrneferst, hbar approach zero, decoherence, just looking at probabilities, quantisation

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**Examples**box, well, tunneling, H atom, double-slit

double-slit weirdness

https://qchu.wordpress.com/2011/07/16/the-heisenberg-picture-of-quantum-mechanics/ -- worked out examples

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**Evolution and unitarity**The energy-time uncertainty principle

https://motls.blogspot.com/2016/03/measurement-isnt-violation-of-unitarity.html

quora.com/What-is-a-tensor-product-in-quantum-mechanics/answer/Charuhas-Shiveshwarkar

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**Open quantum systems**https://en.wikipedia.org/wiki/Open_quantum_system

https://en.wikipedia.org/wiki/Lindbladian

https://en.wikipedia.org/wiki/Belavkin_equation

https://motls.blogspot.com/2017/02/lindblad-equation-cant-solve-any.html

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