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Derivation of the Schrodinger equation

Shan Gao

It is shown that the heuristic "derivation" of the Schrödinger equation in quantum mechanics textbooks can be turned into a real derivation by resorting to spacetime translation invariance and relativistic invariance.

Jan 1, 20100 citations

Heisenberg’s Matrix Mechanics

Alexander Komech

Springer eBooksOct 23, 20120 citations

Heisenberg, Models, and the Rise of Matrix Mechanics

Edward M. MacKinnon

Historical Studies in the Physical SciencesJan 1, 197758 citations

Comment on "Experimental Test of Error-Disturbance Uncertainty Relations by Weak Measurement"

Paul Busch, PEKKA J. LAHTI, Reinhard F. Werner

In this comment on the paper by F. Kaneda, S.-Y. Baek, M. Ozawa and K. Edamatsu [Phys. Rev. Lett. 112, 020402, 2014, arXiv:1308.5868], we point out that the claim of having refuted Heisenberg's error-disturbance relation is unfounded since it is based on the choice of unsuitable and operationally problematical quantifications of measurement error and disturbance. As we have shown elsewhere [PRL 111, 160405, 2013], for appropriate choices of operational measures of error and disturbance, Heisenberg's heuristic relation can be turned into a precise inequality which is a rigorous consequence of quantum mechanics.In this comment on the paper by F. Kaneda, S.-Y. Baek, M. Ozawa and K. Edamatsu [Phys. Rev. Lett. 112, 020402, 2014, arXiv:1308.5868], we point out that the claim of having refuted Heisenberg's error-disturbance relation is unfounded since it is based on the choice of unsuitable and operationally problematical quantifications of measurement error and disturbance. As we have shown elsewhere [PRL 111, 160405, 2013], for appropriate choices of operational measures of error and disturbance, Heisenberg's heuristic relation can be turned into a precise inequality which is a rigorous consequence of quantum mechanics.

arXiv:1403.0367Mar 3, 20141 citation

Heisenberg, matrix mechanics, and the uncertainty principle

S. Lakshmibala

ResonanceAug 1, 20044 citations

Schrödinger Creates Wave Mechanics (1926)

S. Brandt

Abstract The breakthrough to quantum mechanics was, as we have seen in Episode 37, achieved by Heisenberg in the summer of 1925 and the theory, in the form now known as matrix mechanics, was completed a little later by Born, Heisenberg, and Jordan. From his first days as a student Heisenberg had belonged to groups which worked on quantum theory. He was, so to speak, totally immersed in the field and reached his solution at the age of twenty-three. At the turn of the year 1925/26 quantum mechanics was created again, now clad as wave mechanics [1], by Schrödinger, who did not belong to an active research group in the field and who was then thirty-eight. As soon as it appeared wave mechanics was popular with physicists, because it was based on familiar differential equations and not on matrix formalism which was practically unknown.Abstract The breakthrough to quantum mechanics was, as we have seen in Episode 37, achieved by Heisenberg in the summer of 1925 and the theory, in the form now known as matrix mechanics, was completed a little later by Born, Heisenberg, and Jordan. From his first days as a student Heisenberg had belonged to groups which worked on quantum theory. He was, so to speak, totally immersed in the field and reached his solution at the age of twenty-three. At the turn of the year 1925/26 quantum mechanics was created again, now clad as wave mechanics [1], by Schrödinger, who did not belong to an active research group in the field and who was then thirty-eight. As soon as it appeared wave mechanics was popular with physicists, because it was based on familiar differential equations and not on matrix formalism which was practically unknown.

Apr 22, 19920 citations

Translation as heuristics: Heisenberg׳s turn to matrix mechanics

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Translation as heuristics: Heisenberg׳s turn to matrix mechanics

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