Very specific Q's on the P and H operators

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Discussion Overview

The discussion revolves around the origins and formulations of the momentum operator (P) and the energy operator (H) in quantum mechanics, specifically questioning their historical attribution and theoretical basis. Participants explore the relationship between these operators and classical mechanics, as well as seek references for further reading.

Discussion Character

  • Exploratory
  • Technical explanation
  • Historical

Main Points Raised

  • One participant asks who first provided the commonly known spatial and temporal differential forms of the P and H operators, suggesting Schrödinger as a candidate.
  • Another participant asserts that Schrödinger is indeed the one who provided these forms, citing that they reproduce Schrödinger's equation.
  • There is a question about whether these operators depend on the classical mechanics correspondence principle, with a response indicating that the principle was formulated by N. Bohr after observing results from Schrödinger and quantum mechanics in general.
  • References to Schrödinger's original articles published in "Annalen der Physik" in 1926 are provided, detailing specific volumes and pages where the relevant formulations can be found.
  • Participants express a need for access to English electronic versions of the five papers published by Schrödinger in "Annalen der Physik".

Areas of Agreement / Disagreement

There is no consensus on the historical details surrounding the operators, as participants present differing views on the attribution and implications of the correspondence principle. The need for references and access to original papers indicates ongoing exploration rather than resolution.

Contextual Notes

Participants reference specific articles and their content, but there is no agreement on the completeness or accuracy of the historical claims made. The discussion reflects a reliance on various interpretations of quantum mechanics and its historical development.

sifeddin
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I ask very specific Questions on the P momentum operator and the H energy operator:
Who the first gave them their commonly known spatial and timporal differential form? Was he really Schrödinger? On what basis they are so? Is they depend on the classical mechanics correspondance principle/postulate?
Finally I like to get the reference to whatever you knowledgeable poeple of QM reply to me.
 
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sifeddin said:
Who the first gave them their commonly known spatial and timporal differential form?

ERWIN SCHRÖDINGER.

sifeddin said:
Was he really Schrödinger?

No,he was Schrödinger.

sifeddin said:
On what basis they are so?

Because they correctly repreduce Schrödinger's equation.

sifeddin said:
Is they depend on the classical mechanics correspondance principle/postulate?

The principle of correspondance was formulated by N.Bohr,after having seen the results obtained by Schrödinger and,generall,QM.

sifeddin said:
Finally I like to get the reference to whatever you knowledgeable poeple of QM reply to me.

In 1926,in "Annalen der Physik",Erwin Schrödinger published 5 articles (though Weinberg* mentions only 4):
*Vol.79,page 361.
*Vol.79,page 489.
*Vol.79,page 734 (not mentioned by Weinberg*,but part of the footnote on the first page of (**)).
*Vol.80,page 437.
*Vol.81,page 109 (containing in the 6-th section the relativistic Schrödinger equation,according to Weinberg*).

The general ideas and results of these articles (less the relativistic equation) were published by Erwin Schrödinger in English in the American journal:
"The Physical Review",Second Series,Vol.28,No.6,page 1049,Dec.1926 (**)

In this article the correspondence:
[tex]p_{x}\rightarrow \frac{h}{2\pi}\frac{\partial \psi}{\partial x} ,...[/tex]

is found in section #7,page 1064 (of the Journal),in the text between formulas #22 and #23.

And in formula #23 he gives the general classical Hamiltonian as a quadratic form of momenta + the potential energy and then applies the same rule to the classical momenta.
Equation #26 is the generalization of equation #16,the latter giving the time-independent SE for one particle in the potential field V...

Daniel.

-----------------------------------------------------------
* Steven Weinberg,"The Quantum Theory of Fields",CUP,1995,Volume 1,page 40-41.
 
Can anyone help me find an english electronic version of the Annalen der Physik "five" papers
 
help! Again:
Can anyone help me find an english electronic version of the Annalen der Physik "five" papers
 

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