Talk:Schrödinger equation/Archive 1

message: This article is a bit long at the moment I think, perhaps it would be an idea to move the sections Time-independent Schrödinger equation and Schrödinger wave equation into new separate articles, keep the first few lines of text and put this Main article ... at the sections? Passw0rd
: Nope. The article is not particularly long as articles go. Please don't split. -- CYD
: No. The two aspects should appear together. MathKnight 11:13, 14 Nov 2004 (UTC)
thread_title:  splitting the article 

message: I think we should add in the wave equation form of the schrodinger equation, the one in partial differential form as it is far easier to understand at a lower level of mathmatics, and can help people understand the basics of the math in quantum mechanics 
-- Cpl.Luke 18:41, 13 Jun 2005 (UTC)
thread_title:  content 

message: That would be H|p> = 0, and the full SE H|p> = E|p>. E, the energy operator is ih\partial_t. This is not what is now in the article. --MarSch 13:15, 22 Jun 2005 (UTC)
replies: text: Hmm, okay I get it now and will try to clean up a bit.--MarSch 13:19, 22 Jun 2005 (UTC)
thread_title:  time-independent SE 

message: Transfered to copy onto another web.--HydrogenSu 15:04, 5 February 2006 (UTC)
thread_title:  Standing Wave Math Expression 

message: This article needs lower level equations like this:
One dimensional time-independant:
: -\frac{\hbar^2}{2 m} \frac{\mathbf{d^2} \psi (x)}{(\mathbf{d}x)^2} + U(x) \psi (x) = E \psi (x) 
3-dimensional time-independant:
: -\frac{\hbar^2}{2 m} \nabla^2 \psi (r) + U(x) \psi (r) = E \psi (r) 
source: 
:
Not everyone is familiar with bra-ket notation - and the page on bra-ket notation isn't very helpful in learning it. Fresheneesz 09:45, 25 April 2006 (UTC)
replies: text: I agree with this 100%.  The first section presented to the reader should contain the above.  The following sections can then delve into the bra-ket notational version. Ed Sanville 10:21, 25 April 2006 (UTC)
thread_title:  Lower level equations 

message: It would be really instructive to include figures illustrating solutions to the equation, answering questions about how the wave function of that particle that just flew by really looks like, etc. Bromskloss 20:11, 28 April 2006 (UTC)
thread_title:  Illustrations of solutions 

message: In order to organize the many different articles about special case Schrödinger equation solutions, perhaps a template could be created that could be included at the bottom of each of the articles that links to other special case solutions. For example, it could be organized as follows (but with better formatting):
*One dimension:
**free particle
**infinite potential well (particle in a box)
**finite potential well
**delta potential well
**finite potential barrier/square potential
**delta potential barrier
**quantum harmonic oscillator
**particle in a one-dimensional lattice (periodic potential)
**particle in a ring/ring wave guide
*Three dimensions:
**particle in a spherically symmetric potential
**hydrogen atom or hydrogen-like atom
I would make the template myself, but I do not really have much experience with making/using templates like this; also, it would be good to get additional input regarding such a template.--GregRM 14:56, 20 August 2006 (UTC)
thread_title:  Template for special case Schrödinger equation solutions 

message: Members of the Wikipedia:WikiProject Good articles are in the process of doing a re-review of current Good Article listings to ensure compliance with the standards of the Good Article Criteria. (Discussion of the changes and re-review can be found here). A significant change to the GA criteria is the mandatory use of some sort of in-line citation (In accordance to WP:CITE) to be used in order for an article to pass the verification and reference criteria. Currently this article does not include in-line citations. It is recommended that the article's editors take a look at the inclusion of in-line citations as well as how the article stacks up against the rest of the Good Article criteria. GA reviewers will give you at least a week's time from the date of this notice to work on the in-line citations before doing a full re-review and deciding if the article still merits being considered a Good Article or would need to be de-listed. If you have any questions, please don't hesitate to contact us on the Good Article project talk page or you may contact me personally. On behalf of the Good Articles Project, I want to thank you for all the time and effort that you have put into working on this article and improving the overall quality of the Wikipedia project. Agne 00:11, 26 September 2006 (UTC)
thread_title:  GA Re-Review and In-line citations 

message: I have been increasingly noting how entries in WIKIpedia are becoming more heady and obscure instead of being clear as an encyclopedic entry should in fact be.
Contrast the entry here with the following entry I found elsewhere.  
http://www.physlink.com/education/askexperts/ae329.cfm
I think Mathematicians have taken over WIKI and will kill it.
: I agree, the link you provided is the kind of introduction needed for this article. We don't need less math, we need an article that does not begin with a purely mathematical introduction. The heavy lifting should come later. Mathematicians are not a bunch of territorial ogres trying to obscure everything to everyone but themselves. People write what they know, and many people who know the mathematics find it difficult to write a simple introduction because they have taken many steps to get to their knowledge, and its hard to then backtrack and lead someone else along that path. PAR 03:38, 28 September 2006 (UTC)
thread_title:  Can we have less of Maths? 

message: I am reading the article "Improving Student's Understanding of Quantum Mechanics" in the August 2006 Physics Today (which was under some other papers).  The first example of misconceptions is that the time independent Schrödinger equation is true for all states.  To protect against that, maybe this page could be organizes so the time deponent equation appears, without bras and kets, before the time deponent equation does.  That way those who do not know much linear algebra would still see the general form before the stationary state form.  David R. Ingham 20:55, 21 October 2006 (UTC)
thread_title:  Order in which equtions are shown. 

message: : In the mathematical formulation of quantum mechanics, each system is associated with a complex Hilbert space such that each instantaneous state of the system is described by a unit vector in that space.
Since "instantaneous state" of a system extended in space is meaningless in relativity (even special relativity), does this mean tha QM is inherently a non-relativistic theory? —The preceding unsigned comment was added by Pmurray bigpond.com (talk • contribs) 00:29, 5 December 2006 (UTC)
thread_title:  Question: 

message: Currently, the subsection Schrödinger equation#Matrix mechanics and the Schrödinger picture makes it appear wrongly that the equation
:i\hbar{d\hat{A} \over dt} = [\hat{A},\hat{H}]= \hat{A}\hat{H} - \hat{H}\hat{A}
is universally true and consistent with the Schrödinger equation. On the contrary, that equation is only true in the Heisenberg picture (and then only when the partial derivative of A wrt time is zero) while the Schrödinger equation is only true in the Schrödinger picture. Although the two pictures give the same physical results, they are mathematically inconsistent with each other. (They use different bases for the Hilbert space as a function of time.) So any calculation should be done entirely in just one of the two pictures. This article should state at the outset that the Schrödinger equation is part of the Schrödinger picture, not the Heisenberg picture. JRSpriggs (talk) 09:34, 15 March 2012 (UTC)
replies: text: I just moved this to Matrix mechanics without realizing this comment - sorry. -- F=q(E+v×B) ⇄ ∑ici 09:21, 17 March 2012 (UTC)
replies: text: Changes have been made here. I'm still in the process of cleaning up formatting and may re-locate it somewhere else in the article. That section (corrected) is better suited to the Matrix mech article than here.-- F=q(E+v×B) ⇄ ∑ici  09:28, 17 March 2012 (UTC)
thread_title:  Heisenberg picture versus Schrödinger picture 

message: Could you explain to me why atomic number Z is used in the equation in section Schrödinger equation#Two-electron atoms or ions in the kinetic energy term (and the formula for the reduced mass) rather than mass number A (or, more precisely, the mass of the nucleus as a whole including neutrons as well as protons divided by the mass of a proton)? Of course, Z is appropriate in the potential energy term. JRSpriggs (talk) 20:07, 3 April 2012 (UTC)
replies: text: Zmp is the mass of the nucleus, mp is the mass of the proton. For 2-electron atoms mentioned there would be Z protons and... some neutrons. You're right. Lets replace with just M for the mass of the nucleus. F = q(E+v×B) ⇄ ∑ici 20:18, 3 April 2012 (UTC)
replies: text: Fixed. Happy? Sorry for not thinking clearly again (2nd time it happened today, see here)... =( F = q(E+v×B) ⇄ ∑ici 20:22, 3 April 2012 (UTC)
replies: text: Out of interest, isn't the reduced mass usually mu \mu\,\!, not the obscure m_{ep}\,\!? I have yet to see that in a source and arn't we supposed to be using the most common notation? Maschen (talk) 21:14, 3 April 2012 (UTC)
replies: text: Don't remind me of that link - It’s been a bad day today. Does it matter? Greek \mu\,\! is overused, if it annoys you so much why don't you fix it?? F = q(E+v×B) ⇄ ∑ici 21:16, 3 April 2012 (UTC)
replies: text: I will. Maschen (talk) 21:18, 3 April 2012 (UTC)
thread_title:  Atomic weight versus atomic number 

message: I wanted to say something like:-
"Like Newton's second law Schrödinger's equation for a quantum system has not been proved or derived from more elementary principles. It is used because it works and has predicted a multitude of reactions time and time again - the only proof is in nature or natural."
Blueawr (talk) 07:55, 1 September 2012 (UTC)
replies: text: You could put that in somewhere, but it is the kind of statement that needs to be backed up with a good secondary source. RockMagnetist (talk) 16:53, 1 September 2012 (UTC)
thread_title:  Introductory Preamble 

message: I have proposed before (in passing) that we make an article on the exact solutions (and forgot, till now), such as Schrödinger equation (exact solutions), because;
*it will trim the article (currently 81.527 kB, too big)
*reduces the amount of maths in this article, allowing for more qualitative content future editors may add,
*parallels the nice idea of Exact solutions in general relativity from Einstein field equations,
*helpful for those just introduced to the equation, since there will not be many realistic systems it can be solved for exactly, and serves as a springboard to perturbation theory (quantum mechanics), variational method (this article is for QM), ladder operators...
written summary style for detailed articles on specific systems (step potential, delta potential, Harmonic oscillator (quantum), hydrogen atom etc.). Any objections? Maschen (talk) 09:59, 11 November 2012 (UTC)
replies: text: Update: I'm drafting this in a pre-article (in namespace), it will not be created if people desire to re-merge in the future... Maschen (talk) 18:11, 1 December 2012 (UTC)
thread_title:  Separate article on exact solutions? 

message: Something should be mentioned concerning the use of the equation to scattering problems by partial wave analysis.--188.26.22.131 (talk) 12:31, 2 August 2013 (UTC)
thread_title:  Partial waves method 

message: In response to the above thread...
I proposed before (more than once now) to transfer the exact solutions of the Schro eqn to a separate article Schrödinger equation (exact solutions). Note also the main article quantum mechanics has overlap on exact solutions to the non-relativistic Schro equation. Would cutting out the "exact solution" sections in this article and the QM article be useful?
Or instead, we could just transfer all of the non-relativistic formalism to another article: Schrödinger equation (non-relativistic) (by all means correct me on the dashes, this is just a suggestion...). This may have been proposed by someone before also... 
Maybe both? In Schrödinger equation (non-relativistic), we have a discussion of the general ideas of the non-relativistic case, leading onto the mathematical details (such as those in the "properties" section of this article), without the exact solutions, then linking to the Schrödinger equation (non-relativistic) article.
Any thoughts? M∧Ŝc2ħεИτlk 20:36, 25 September 2013 (UTC)
replies: text: Update: see also this section. M∧Ŝc2ħεИτlk 12:51, 27 September 2013 (UTC)

text: I just realized there is the article List of quantum-mechanical systems with analytical solutions. So there is no need for a new article. M∧Ŝc2ħεИτlk 09:16, 27 January 2014 (UTC)
thread_title: Split off the non-relativistic content to another article(s)?

message: I guess the article is missing the key concept of axiomatic derivation of the Schrodinger's equation using the time evolution operator. This is the most natural and modern approach to understanding the equation (although, most likely, not originally proposed by Schrodinger). The details can be found, for example, in "Modern Quantum Mechanics" by J. J. Sakurai or this lecture by Prof. Susskind. -  Subh83 (talk | contribs) 22:07, 21 February 2014 (UTC)
thread_title:  Axiomatic construction using time-evolution operator 

message: http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation#Constant_potential
I was going to cut part of a sentence, but I decided to associate it with the following sentence so it'd flow right and not cause the misapprehension that made me thik of cutting it.
68.2.82.231 (talk) 17:54, 10 May 2014 (UTC)
replies: text: Actually, now that I've edited it, I think the text doesn't really go with the picture. It sounds like it's describing a particle in a box, not a particle impinging on a single wall. I'll think more and maybe improve on it later. If there's an equally good animation of the particle in a box, this paragraph could be used with it in a new section (maybe collapsed a bit since it's somewhat redundant). 68.2.82.231 (talk) 18:01, 10 May 2014 (UTC)
thread_title:  Distance and potential confused in Constant Potential section 

message: I never noticed this untill now. Someone in the lead has made the claim:
:"But Schrödinger's equation, although often presented as a postulate, can in fact be derived from symmetry principles."
with the citation to the book:
:</ref>
So apparently the SE is not a postulate but can be "derived". Is this a misunderstanding of the editor who added the citation? Is the author of the book making a non-mainstream claim? Why would so many other sources treat the SE as a postulate while this random textbook says it can be derived? 
I suggest removing it, could be WP:OR. M∧Ŝc2ħεИτlk 10:12, 14 September 2014 (UTC)
replies: text: ...or at least rewriting it, saying that some authors say it is a postulate while others consider it to be derivable, and for the latter case what the foundations are to "derive" it from symmetry principles (most likely it is justified by symmetry principles, but I could be wrong). I may be very picky - but this is an important point to make clear about the equation. M∧Ŝc2ħεИτlk 21:41, 15 September 2014 (UTC)
replies: text: When one works backwards and takes the symmetries of an equation and adds the necessary constraints, you can derive almost anything.  In this case the required symmetry is presumably Galilean relativity, and a constraint to a scalar field, conservation of energy and a perhaps a few others ... I don't think that it belongs in the lead. —Quondum 01:17, 16 September 2014 (UTC)
replies: text: In the lead we need to state at the outset whether or not the equation is a postulate or a derivable equation. These are two different things. There have been a number of confused edits to the article (and likely other QM articles) which assert the SE can be derived. First I'll wait for more opinions before making changes. M∧Ŝc2ħεИτlk 20:46, 26 September 2014 (UTC)

text: Well, actually I made the changes anyway, along my own proposal since no one has objected, but when possible input from others would still be very helpful. M∧Ŝc2ħεИτlk 23:47, 26 September 2014 (UTC)
thread_title:  "Derived from symmetry principles"?? 

message: In a lot of the equations it doesn't specify the meanings of all the variables. This isn't "quantum physics experts we already know all this" wiki. Every variable should be specified as to what it means.35.8.84.29 (talk) 19:52, 22 October 2013 (UTC)
replies: text: For almost every equation the variables are specified, and there are links to the related articles like De Broglie relations and partial differential equations. Nevertheless, I agree there are some notational gaps (such as partial derivatives - reverse "6"), and will try to fill them in. M∧Ŝc2ħεИτlk 15:27, 23 October 2013 (UTC)

text: Done. Please point out any specific equations which lack definitions of symbols. Thanks, M∧Ŝc2ħεИτlk 15:43, 23 October 2013 (UTC)
thread_title:  Fails to Specify Variables 

message: Schrödinger field theory handles particles as part of the same wavefunction, and time degrades distance in order the spin of the particles is maintained. Particles are treated as "sacks of noise spots" a discrete mathematics approach. No extra particles needed, but in order the Schrödinger Equation describes all particles as parts of the same wider and complex wavefunction, particles should be considered as "noise sacks". Discrete mathematics and combinatorics needed to express the "entropic degradation of distance due to time" and the overall urge of achieving a "mean inner time perception of the particles of a gravitational system"  — Preceding unsigned comment added by 2.84.209.134 (talk) 07:17, 30 May 2015 (UTC)
thread_title:  Schrödinger field theory vs Graviton 

message: Removed the metaphysical waffle of "...can be in several different locations at the same time...". That sort of description has no basis in standard quantum mechanics. Any experiment that can only be interpreted as a particle in two positions, would constitute an actual measurement of a particle having two eigenvalues at the same time. However, such a measurement would falsify a basic postulate of QM that requires all measurements to result in a single eigenvalue. The basic issue here is that QM is quantum, not classical. A classical argument might well result in such nonsense, but its not part of QM.  — Preceding unsigned comment added by Kevin aylward (talk • contribs) 10:24, 30 August 2015 (UTC)
thread_title:  "Simultaneous Positions" 

message: Added a Ballentine sourced quote that illustrates the fundamental issue with claiming that particles are really waves. It should be noted that there is absolutely no disagreement in standard quantum mechanics that there is only one wave equation for a multi particle system. For example, the Debroglie wavelength of a molecule is a single number, irrespective of the fact that may be several sub particles. This wavelength may be either much larger or much smaller than the size of the molecule. Quantum mechanics simply don't work by imagining little wave packets for each particle. dah...Kevin Aylward 08:23, 6 September 2015 (UTC)
thread_title: "Only One Wave Equation"

message: Noticed that r is not defined, I am making the assumption that r is the radius along the axis of wave propagation, but formally r should be defined. PB666 yap 12:22, 25 March 2016 (UTC)
thread_title:  r in the equations goes undefined 

message: In Dublin in 1952 Erwin Schrödinger gave a lecture in which at on point he jocularly warned his audience that what he was about to say might "seem lunatic". It was that, when his equations seem to be describing several different histories, they are "not alternatives but all really happen simultaneously". This is the earliest known reference to the multiverse (David Deutsch, The Beginning of infinity, page 310). Kartasto (talk) 11:22, 16 April 2016 (UTC)
thread_title:  Multiverse 

message: Apart from inserting a derivation of the equation (see above), I have also removed the incorrect statement that Schrödinger's equation is inconsistent with quantum field theory. Perhaps the editors who inserted this meant that it is impossible to write down a Hamiltonian for a single particle consistent with special relativity. However, quantum field theory is still based on Schrödinger's equation, except that the wave-function must be defined on the Fock space. Alternately, one may consider wave-functions on field configurations. In fact, even in extensions of quantum field theory like string theory, Schrödinger's equation is not modified. Jacob2718 (talk) 09:07, 4 December 2016 (UTC)
thread_title:  Consistency with QFT etc.