Talk:Making sense of quantum mechanics

Lessons on the principles of Quantum Mechanics
Wikiversity has not yet lessons on the Principles of Quantum Mechanics. There is a Study guide:Quantum mechanics I. I think we need some lessons on the first principles and the basic postulates presented in a logical sequence, kind of: I found that the french lessons on the postulates of Quantum Mechanics are well presented. Maybe I could take inspiration of their templates? Arjen Dijksman 10:32, 15 September 2007 (UTC)
 * Quantum Mechanics is based on the fact that physical systems are represented by vectors (also called state vectors or kets, as introduced by Dirac), contrary to Classical Mechanics where systems are represented by collection of points on which forces act. This is the central postulate of Quantum Mechanics.
 * As systems are represented by vectors, Quantum Mechanics focuses on the orientation (phase, angle...) of those vectors, and not on the classical properties as position or velocity. We may then deduce the law of motion for quantum systems: time evolution is an evolution of the phase of the vector, which gives the time-dependent Schrödinger equation. In conventional presentations of Quantum Mechanics, this time evolution law is generally postulated independently.
 * We may then introduce the observational aspects. Observing something on a quantum system means that it interacts with another quantum system. The outcome of an interaction by two systems represented by vectors (linear segments) is undetermined depending on the place of interaction: principle of indeterminacy (Heisenberg). An interaction means that something operates on the vector: observational postulate.
 * and so on...


 * I think Bra-ket notation is a good example of Wikipedia resources for physics. That encyclopedia article is written by people who know the topic and for other people who know the topic. The article does not adequately explain the jargon that is used and does not offer a learning path for helping non-experts towards understanding the topic of the article. I wonder if "first principles" (above, on this page) is meant to include details like explaining jargon (such as "kets"), or not. --JWSchmidt 15:58, 15 September 2007 (UTC)


 * Yes, a first principles lesson written by contributors of this Making sense of quantum mechanics Project would be meant to either avoid specialized jargon and notations either include some intuitive explanation of it. Kets would for example simply be presented as rotating arrows or rods or needles or baseball bats or any ordinary objects that have an extent and a direction in some space. Would that make sense? Arjen Dijksman 19:52, 15 September 2007 (UTC)
 * That sounds good....analogies are useful for introducing people to new ideas. Another problem I have with many presentations of mathematical physics is that it seems like extra points are awarded to authors for concocting the most concise and general descriptions of topics, but such descriptions are of little use to people trying to learn the subject. I started thinking about this issue when I saw "physical systems are represented by vectors". I wished there was a link right there leading to several specific examples. --JWSchmidt 20:14, 15 September 2007 (UTC)
 * We need indeed some figures with arrows illustrating physical systems. Arjen Dijksman 21:37, 15 September 2007 (UTC)
 * I'd be glad to try making some images if I had an idea what is needed. This might be a good time to start making use of the Digital media workshop. --JWSchmidt 22:00, 15 September 2007 (UTC)

++== Time evolution of state vector ==++

Here is a sketch for an image that could illustrate the Schrödinger equation (I am horrible in graphics:- Arjen Dijksman 23:00, 15 September 2007 (UTC)
 * I could make a new version of this figure, but I do not understand the figure. --JWSchmidt 23:39, 15 September 2007 (UTC)
 * This figure could illustrate the fact that the vector difference $$|\psi(t+\Delta t) \rangle - |\psi(t) \rangle$$ between a needle at instant $$ t $$ and the same needle at instant $$ t + \Delta t $$ is perpendicular to the state vector $$ |\psi(t) \rangle $$ at instant $$ t $$ and proportional to the angular velocity $$ \omega $$ of the needle, for very small $$ \Delta t $$. In equation form, this may be stated as:

$$(|\psi(t+\Delta t) \rangle - |\psi(t) \rangle) \ \ \bot \ \ |\psi(t) \rangle \ \ $$   for    $$ \ \ \Delta t \rightarrow \ 0$$


 * and

$$(|\psi(t+\Delta t) \rangle - |\psi(t) \rangle) \ \ = \ \ i \ \omega \ |\psi(t) \rangle \ \Delta t \ $$   for    $$ \ \ \Delta t \rightarrow \ 0$$


 * provided that the time axis points towards us out of the plane of the screen. Maybe this could be stated in a better understandable way? Unfortunately there are some symbols needed. Arjen Dijksman 05:23, 16 September 2007 (UTC)
 * I learned the basics of vectors, inner products and quantum mechanics when I was in college, but I was never taught the notation that you are using. --JWSchmidt 20:29, 18 September 2007 (UTC)
 * Yes, this is Dirac's notation. I'll look for different manners to describe in what $$ \vec {\psi} $$ and $$|\psi \rangle $$ differ. $$ \vec {\psi} $$ is an ordinary static vector in 3D. $$|\psi \rangle $$ is also a vector (=arrow) but with physical properties attached to it: a state vector (or ket). This makes it suited to describe a physical linear object. It evolves or interacts with the physical environment. There is a physical relationship between $$|\psi (x_1) \rangle $$ and $$|\psi (x_2) \rangle$$, $$x_1$$ and $$x_2$$ being any physical observable. Describing this relationship for different conditions forms the object of Quantum Mechanics. Arjen Dijksman 22:10, 18 September 2007 (UTC)


 * What do you think about Quantum Mechanics and This quantum world? --JWSchmidt 22:27, 18 September 2007 (UTC)
 * Both texts are fine as they guide us through various aspects of Quantum Physics. The first text needs to be completed. I did not yet manage to read This quantum world at full extent. I appreciate its illustrations that help to visualize now and then the presented concepts. I also appreciate the fact that it deals with interpretational issues like the Bohmian view and Bell's theorem. Both texts present Quantum Mechanics from the viewpoint of its historical development. The first introduces QM with wave mechanics and the second explaining how classical serious illnesses require drastic remedies. That's the conventional approach in which QM is presented. From experience, you need to read dozens (if not dozens of dozens) of these texts combined with experimental and theoretical practice before gaining some intuitive comprehension of QM. In this way, it is very difficult to make QM accessible to a larger public. That's why I am looking for intuitively clear approaches to Quantum Mechanics, starting with the simplest elementary bricks, like a single photon, or electron, before extending to the behaviour of quantum wave mechanics or quantum fields. Arjen Dijksman 07:46, 22 September 2007 (UTC)

We could be a bit more general for the evolution law of state vectors, focusing only on the angle (the phase $$\phi$$). We could write a general differential equation:

$$|\psi(\phi+\Delta \phi) \rangle - |\psi(\phi) \rangle \ \ = \ \ i \ \ |\psi(\phi) \rangle \ \Delta \phi \ $$   for    $$ \ \ \Delta \phi \rightarrow \ 0$$

where $$\Delta \phi$$ could be understood as $$\omega \Delta t$$, but also $$k \Delta x$$ for situations where the angle changes when we shift the arrow a bit in the x-direction (k being the wavenumber, i.e. the angle through which the arrow would rotate if the arrow is shifted over unit length), or even some $$t_0 \Delta \omega$$, if we focus on a change of angular velocity at a given instant $$t_0$$. Arjen Dijksman 16:00, 6 October 2007 (UTC)

Navigation template
I made the page Template:Quantum mechanics and you can add it to pages using:. --JWSchmidt 19:31, 18 September 2007 (UTC)

Operators operate an ordinary arrows giving other ordinary arrows
I have started to write the text for the third principle about operators and the way they act on state vectors. I have some difficulty to describe it without reference to the abstract formalism, while it seems relatively ordinary: you have an arrow, you rotate it in some way (constrained or free) or you subtract it from another arrow. You always obtain another arrow. These arrows relate one to another with proportionality factors depending on the physical properties of the system. The relation is represented by mathematical formalism where appear complex exponentials and the observables (speed, spinning direction, energy, potentials...). So the behavior is intuitive but the formalism makes it abstract. Anyone has some ideas on the subject? Arjen Dijksman 17:43, 6 October 2007 (UTC)