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Quantum Theory

Lectures on theoretical physics by H.A. Lorentz

By H.A. Lorentz

LECTUEES ON THEOBETICAL PHYSICS brought on the college OF LEIDEN via H. A. LORENTZ authorized TRANSLATION via L SILBERSTEIN, Pir. I., AND A. P. Jl. TKIVKLLl quantity I AETHER THEORIES AND AETHER versions EDITED UY II. BREMEKAMP, Pn. I. KINETICAL difficulties EDITED JBY E. D. BRUINS, Pu. D., AND J. REUDLER, Pii. D. Osmania collage HYO - i. MACMILLAN AND CO., restricted ST. MARTINS road, LONDON 1927 COPYRIGHT revealed IN nice BRITAIN through It. ok. CLARK, constrained, EDINBURGH PREFACE TO THE ENGLISH TRANSLATION a chain of admirably transparent and instructive classes of lectures, protecting primarily nearly the entire box of Theoretical Physics, have been added by way of Professor Lorenf z on the college of Leiden. Seven of those classes, pertaining to matters of basic value, have been, as much as 1922, edited through Lorentzs students and released within the Dutch language. in the course of Professor Lorentzs stopover at within the usa in 1922 the plan used to be conceived to make those classes of lectures available to. English readers. After a few hold up necessitated by means of situations the current quantity I. is being issued. It includes the English model of 2 of those classes of lectures, viz. Aether Theories and Aether versions, edited within the Dutch language via Prof. H. Bremekamp, and Kinetical difficulties, edited by means of Dr. E. D. Bruins and Dr. J. Heudler. to maintain the abnormal attraction of Lorentzs personal type and exposition the interpretation of those lectures has been made as literal as was once appropriate with the character of the English language. just a only a few adjustments or explanatory additions have been made within the textual content. The latter are put in sq. brackets. Volumes II. and III., now in guidance, will comprise the rest 5 lecture classes, particularly, Thermodynamics, Entropy and chance, idea of Radiation, thought of Quanta, and the main of Relativity for Uniform Translations distinctive conception of Relativity. lately, 1925, yet one more process lectures, on Maxwells concept, was once introduced out at Leiden, and preparations could be made to incorporate its English model into this ebook. L. S. A. P. H. T. ROCHESTER, N. Y., July 1926. CONTENTS AETHER THEORIES AND AETHER versions I. ABERRATION of sunshine PACK 1. Stokes 1 concept The Earth drags the encircling Aether . . three 2. pace power in an Incompressible Aether ... 6 three. Plancks thought. Compressible Aether .... 7 four. Fresnels conception. fastened Aether ..... 12 five. Dragging Coefficient ....... thirteen 6. conception of Aberration ....... 14 7. Michelsons scan . . . . . . .19 eight. Contraction towards movement ..... 23 II. MECHANICAL AETHER THEORIES nine. Maxwells Equations ....... 24 10. The Magnetic strength as pace. Neumanns concept of sunshine . 26 eleven. the electrical strength as speed. Fresnels idea of sunshine . . 29 12. thought of Elasticity. McCullaghs Aether .... 30 thirteen. Quasi-rigid Aether 31 14. Quasi-labile Aether ....... 35 15. Graetzs idea ........ 36 sixteen. The Charging of a Conductor in accordance with the Elastic Aether Theories ......... 37 III. KELVINS version OF THE AETHER 17. Kelvins version of the Quasi-rigid Aether .... forty 18. stable Gyrostat forty four 19. Liquid Gyrostat ........ forty eight 20. Liquid in Turbulent movement as Aether version .... fifty two IV. charm AND REPULSION OF PULSATING SPHERES 21. Nature of the matter fifty eight 22. A unmarried relocating Sphere ....... fifty nine 23. A Sphere at leisure in a Liquid with a given movement ... 60 24. n Spheres ......... sixty one 25. Spheres ........ sixty two 26. remedy of the matter via Lagranges Equations . sixty five 27. Pearsons conception ........ sixty seven resources AND REFERENCES ...... 70 vii viii CONTENTS KINETICAL difficulties PAOR advent ......... seventy five bankruptcy I internal FRICTION AND SLIDING, handled HYDRODYNAMICALLY 1. Hydrodynamical Equations of an Incompressible Viscous Liquid . seventy seven 2. influence of Sliding upon a Liquid flowing in a Tube ... eighty three. The Dragging of a Liquid by way of a relocating Plate .... eighty one four. influence of Sliding relating to Translational movement of a Sphere in a Liquid ......... eighty three 5...

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This method originated with Schrodinger,3 who was able to show that for an electron with the charge-e moving in the field of a fixed nucleus of charge +Ze (hydrogenlike atom), for which the potential energy is V = -(Ze 2/r), the negative, discrete energy eigenvalues -Rh/1 2, -Rh/2 2, ••• , -Rh/n 2, ••• and the adjacent, continuous. positive energy eigenvalues (0 -~ E < + oo) follow from his wave equation Icf. du+ In the above ( e•) z u=O. E+-rme' R = - -1Z1 4n1l. is Rydberg's constant multiplied by the square of the charge of the nucleus.

This question was again discussed by G. Jaffe, Z. Physik 66, 770 (1930). It appears to us, however, that the most general answer to the question is given in the above paper of von Neumann. " Sec. 6. Stationary States as Eigenvalue Problem 43 functions u, v: J v* (H u) dq. = J u(Hv)* dq. d9 not disturb the "Hermiticity" of Hby having singular points, are permitted to be solutions of eq. 3). 4) should hold, if one of the two functions is regular. We can make still more general assumptions regarding the domain of values of q and the range of the function u.

17') the rules regarding the mean values of Pk and xk and the total current i k = f ikd3x and their time derivatives follow, which are analogous to the corresponding equations of motion of classical mechanics. 14) again a continuity equation :, ('P*'P) + divi = 0, which at the same time verifies that H is Hermitian. 22') (which corresponds to eq. 16'). 6) and (4. 19) 30 General Principles of Quantum Mechanics Sec. 4. so that the symmetry condition T1c1 = T 11, is again fulfilled. 23) m --;[12 = K 11 • as the analogue of the equation of motion.

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