User talk:80.163.26.74

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By mistake I put the following two comments first on the user page, instead of the discussion page where they belong. I am sorry about that.--P.wormer 09:48, 13 August 2007 (UTC)

(i) So, professor, why don't you contribute something to the article on the Schroedinger equation? Or at least remove the grossest errors? --P.wormer 05:53, 13 August 2007 (UTC)

I am confident that the article will propagate and in the end be a very good one. I am not a native speaker/writer, and a lot of people are doing very good.

(ii) You wrote:

and the use of the Dirach's notation is throughout the article completely wrong.

This statement intrigued me, so I checked the reputable book of Messiah (p.312). He writes

i\hbar \frac{d}{dt} |\psi(t)\rangle = H|\psi(t)\rangle
I know this book, and I like it. Explain for me why ψ(t) is enclosed in a "ket". You refer to page 312, so I assume Messiah who had introduced the Schrödinger equation far before in his book, now uses a "ket", for some specific reasons? I can not remember why (I will find out), but maybe just to explain an example of a "ket"?

I also checked Dirac's book (p. 110). He uses a slightly different notation (P instead of ψ no brackets around t):

Which book? And you are sure that P is same as ψ? in P t\rangle? It is not! (Please also notice, that the equations you refer to is about a "Hamiltonian" and not a Schrödinger-operator)). I am completely sure that you misinterpret Dirach if you think that P is the same as ψ. A "ket" denotes in general a state "without any representation". This is in contrast to the "wave function ψ" which is a function in time and space. It represents a state in "position space".
In the Dirach notation the presentation comes by applying the "brac" on the "ket" in terms of an "overlap":
A "ket" presents a "state" which can be presented by "overlaps" of other states. The overlap states are denoted "brac"s. So for instance we have for the (one-dimensional) position state |x' \rangle, that it in position space can be presented as
\langle x|x' \rangle =\delta (x-x')
while it in "momentum space" is given as
\langle p|x' \rangle =\frac{1}{2\sqrt \pi}\exp(i p/\hbar x)


So, at least the time-dependent Schrödinger equation is written correctly in the Dirac notation in the article. I am curious to hear from you what the completely wrong parts are?

Of course the Schrödinger equation, time dependent or not, can be expressed by Dirac notation. The same yield for a lot of other differential equations. A "ket" can denote anyhing. And so can a "brac". And the "bracket" is the "overlap" between the "brac" and the "ket" state. In contrary to this ψ is a spatial solution to the Schrödinger equation.
To put a wave function ψ into a "ket" which afterwards is inserted into the Schrödinger equation is nonsens! (at least without a proper explanation). And at present, this is the very first equation in the Wikipdia-article. And by the way Schrödinger did not know anything about the "Dirac notation". What did he know? He based his equation on the following:
  1. E= \hbar \omega (Planch/Einstein)
  2. P= \hbar k where k is the wavenumber (Luis de Broglie)
  3. E= \frac{1}{2}mv\cdot v +V(Newton)
Besides these physical observations, he could by looking at the harmonic wave function exp(i(kx − ωt)), see that the wave number k and the frequency ω can be obtained as eigenvalues by applying differential operators, which inserted into the Newton equation above, finally ends up in the Schrödinger equation. Sincirely j.h.povlsen80.163.26.74 00:28, 15 August 2007 (UTC)
--P.wormer 09:48, 13 August 2007 (UTC)

[edit] Dead links in Mandriva article

Thank you very much for the information you provided. I've fixed all the easy ones. Cheers, CWC 17:52, 31 October 2007 (UTC)