The role of equivalence in Quantum Mechanics

Alexander S. Blum, Martin Jähnert

Abstract This paper re-evaluates the formative year of quantum mechanics—from Heisenberg’s first paper on matrix mechanics to Schrödinger’s equivalence proof—by focusing on the role of radiation in the emerging theory. We argue that the radiation problem played a key role in early quantum mechanics, a role that has not been taken into account in the standard histories. Radiation was perceived by the main protagonists of matrix and wave mechanics as a central lacuna in these emerging theories and continued to contribute to the theoretical development and conceptual clarification of quantum mechanics. Studying the interplay between quantum mechanics and radiation, the paper provides an account of (a) how quantum mechanics was able to connect to its empirical basis in spectroscopy and (b) how Schrödinger’s equivalence proof emerged from his explorative calculations on the emission of radiation.

C. JAYARATNAM ELIEZER, P. G. L. Leach

E. R. Tuttle

A simple method is given for finding the values of the total angular momentum J for configurations of equivalent electrons in jj coupling. It is also shown how a knowledge of both the LS and jj terms can contribute to the student’s understanding of the role of different representations in elementary quantum mechanics. Because the principles and the computations required are elementary, this material is particularly suitable for presentation to undergraduates and to graduate students taking a first course in quantum mechanics.

P. C. W. Davies

Alon E. Faraggi, Marco Matone

Τ. Padmanabhan

The role played by general relativity in quantum mechanics (especially as regards the uncertainty principle) is investigated. It is confirmed that the validity of time-energy uncertainty does depend on gravitational time dilation. The author also shows that there exists an intrinsic lower bound to the accuracy with which acceleration due to gravity can be measured. The motion of the equivalence principle in quantum mechanics is clarified.