Ettore Majorana

by Majorana, Ettore; Esposito, Salvatore; Van Der Merwe, Alwyn; Recami, Erasmo

• ISBN13: 9781402016493
• ISBN10: 1402016492
• Format: Hardcover
• Copyright: 2003-11-01
• Publisher: Kluwer Academic Pub

Summary

This book is unique, since it reveals the outstanding personality underlying Majorana's notes. An extraordinary mixture of mathematical command, physics intuition and creative thought makes the Notes enjoyable for physicists of every discipline. The Notes are interesting for both graduate students and theoretical physics experts. In fact, the contents range from applied physics models, thorough fundamental atomic physics, to advanced group theory. The Notes have never been published and here they appear in the same format as organized by Ettore Majorana. The style is plain, proposed solutions to physics problems are original. These notes are intended as a series of fundamental physics themes treated by Ettore Majorana during the first "burning years" of the Panisperna Group, as the new deal of physics started in Rome around Enrico Fermi.

Table of Contents

Preface	xiii
References	xxv
Volumetto I	1	(84)
1 Electric potential	1	(3)
2 Retarded potential	4	(1)
3 Interaction energy of two electric or magnetic charge distributions	5	(1)
4 Skin effect in homogeneous cylindrical electric conductors	6	(4)
5 Thermodynamics of the thermoelectric cells	10	(1)
6 Energy of an isolated conductor	11	(1)
7 Attraction between masses which are far apart	12	(2)
8 Formulae	14	(1)
9 Electric lines	15	(3)
10 Density of a spherical mass distribution	18	(1)
11 Limit skin effect	18	(5)
12 Limit skin effect for simply-shaped conductors. Hints for arbitrary shapes	23	(3)
12.1 Elliptic cross sections	23	(1)
12.2 Effect of the irregularities of the boundary	24	(2)
13 Hysteresis in magnetic conductors in the limit skin effect regime	26	(2)
14 Field produced by a circular and homogeneous distribution of charges in its own plane	28	(1)
15 Field produced by a circular charge current in a plane	29	(1)
16 Weak skin effect in conductors, with an elliptic cross section, having the same magnetic permeability as the surrounding medium	30	(1)
17 Oscillating discharges in capacitors	31	(1)
18 Self-induction of a very long circular coil with many turns	32	(1)
19 Energy of a uniform circular distribution of electric or magnetic charges	33	(3)
20 Self-induction in a rectilinear coil with finite length	36	(2)
21 Mean distances of volume, surface, or line elements	38	(1)
22 Evaluation of some series	39	(2)
23 Self induction of a finite length rectilinear coil with circular cross section and a finite (small) number of turns	41	(2)
24 Variation of the self-induction coefficient due to the skin effect	43	(2)
25 Mean error in estimating the probability of an event through a finite number of trials	45	(1)
26 Unbalance of a pure three-phase system	46	(1)
27 Table for the computation of z!	47	(1)
28 Influence of a magnetic field on the melting point	48	(2)
29 Specific heat of an oscillator	50	(2)
30 Do children of the same parents tend to be of the same sex?	52	(1)
31 Heat propagation from a certain cross section along an infinite length bar endowed with another cross section acting as a heat well. A similarity with the crickets	53	(2)
32 Combinations	55	(1)
33 Energy and specific heat of a rotator	56	(2)
34 Gravitational attraction of an ellipsoid	58	(5)
35 Special cases: prolate ellipsoid and spheroid	63	(3)
36 Equilibrium of a rotating fluid	66	(3)
37 Definite integrals	69	(2)
38 Heat propagation in an isotropic and homogeneous medium	71	(3)
38.1 One-dimensional propagation	71	(3)
39 Conformal transformations	74	(3)
40 Wave mechanics of a mass point in a conservative field. Variational approach	77	(1)
41 Electromagnetic mass of the electron	78	(4)
42 Legendre polynomials	82	(1)
43 V2 in spherical coordinates	83	(2)
Volumetto II	85	(120)
1 V2 in cylindrical coordinates	85	(1)
2 Expansion of a harmonic function in a plane	85	(2)
3 Quantitation of a linear harmonic oscillator	87	(3)
4 Diagonalization of a matrix	90	(3)
5 Wave quantitation of a point particle that is attracted by a constant force towards a perfectly elastic wall	93	(4)
6 Relativistic hamiltonian for the motion of an electron	97	(4)
7 The Fermi function	101	(4)
8 The interatomic potential without statistics	105	(3)
9 Application of the Fermi potential	108	(3)
10 Statistical behavior of the fundamental terms in neutral atoms	111	(1)
11 Numbers to the fifth power	112	(1)
12 Diatomic molecule with identical nuclei	113	(1)
13 Numbers to the sixth power	114	(1)
14 Numbers to the seventh power	115	(1)
15 Second approximation for the potential inside the atom	116	(1)
16 Atomic polarizability	117	(1)
17 Fourier expansions and integrals	118	(2)
18 Blackbody	120	(1)
19 Radiation Theory (Part 1)	121	(6)
20 Moment of inertia of the Earth	127	(4)
21 Radiation Theory (Part 2)	131	(2)
22 About matrices	133	(2)
23 Radiation Theory (Part 3)	135	(2)
24 Perturbed keplerian motion in a plane	137	(7)
25 Radiation Theory (Part 4)	144	(2)
26 Definite integrals	146	(2)
27 Series expansions	148	(2)
28 Radiation Theory (Part 5): free electron scattering	150	(4)
29 De Broglie waves	154	(1)
30 e2 = hc?	155	(1)
31 The equation y" + Py = 0	156	(4)
32 Indeterminacy of vector and scalar potentials	160	(1)
33 On the spontaneous ionization of a hydrogen atom placed in a high potential region	161	(16)
34 Scattering of an &alpa; particle by a radioactive nucleus	177	(11)
35 Retarded potential	188	(2)
36 The equation y" = xy	190	(1)
37 Resonance degeneracy for many-electron atoms	190	(2)
38 Various formulae	192	(13)
38.1 Schwarz formula	192	(1)
38.2 Maximum value of random variables	193	(2)
38.3 Binomial coefficients	195	(1)
38.4 Expansion of 1/(1 - x) n	196	(1)
38.5 Relations between the binomial coefficients	197	(1)
38.6 Mean values of rn between concentric spherical surfaces	198	(7)
Volumetto III	205	(114)
1 Evaluation of some series	205	(2)
2 The equation H = r	207	(5)
3 Equilibrium of a rotating heterogeneous liquid body (Clairaut problem)	212	(14)
4 Determination of a function from its moments	226	(9)
5 Probability curves	235	(2)
6 Evaluation of the integral |0π/2 sinkx/sinx dx	237	(4)
7 Infinite products	241	(1)
8 Bernoulli numbers and polynomials	242	(1)
9 Poisson brackets	243	(5)
10 Elementary physical quantities	248	(2)
11 "Chasing the dog"	250	(2)
12 Statistical potential in molecules	252	(3)
13 The group of proper unitary transformations in two variables	255	(10)
14 Exchange relations for infinitesimal transformations in the representations of continuous groups	265	(2)
15 Empirical relations for a two-electron atom	267	(4)
16 The group of rotations 0(3)	271	(5)
17 The Lorentz group	276	(3)
18 Dirac matrices and the Lorentz group	279	(8)
19 The spinning electron	287	(11)
20 Characters of Dj and reduction of Dj X D'j	298	(3)
21 Intensity and selection rules for a central field	301	(6)
22 The anomalous Zeeman effect (according to the Dirac theory)	307	(4)
23 Complete sets of first-order differential equations	311	(8)
Volumetto IV	319	(100)
1 Connection between the susceptibility and the electric moment of an atom in its ground state	319	(3)
2 Ionization probability for a hydrogen atom in an electric field	322	(7)
3 Expansion of Legendre polynomials in the interval -1 less than or equal to x less than or equal to 1 329
4 Multiplication rules for Legendre polynomials	329	(1)
5 Green functions for the differential equation y"+(2/x -1) y + ø(x) = 0	330	(3)
6 On the series expansion of the integral logarithm function	333	(2)
7 Fundamental characters of the group of permutations of objects	335	(4)
8 Expansion of a plane wave in spherical harmonics	339	(3)
9 The Rutherford formula deduced from classical mechanics	342	(3)
10 The Rutherford formula deduced as a first approximation to the Born method	345	(3)
11 The Laplace equation	348	(2)
12 Polarization forces between hydrogen atoms	350	(2)
13 Integral representation of the Bessel functions	352	(3)
14 Cubic symmetry	355	(3)
15 Formulae	358	(1)
16 Plane waves in the Dirac theory	359	(10)
17 Improper operators	369	(3)
18 Integral representation of hydrogen eigenfunctions	372	(2)
19 Deflection of an alpha ray induced by a heavy nucleus (Classical Mechanics)	374	(1)
20 Scattering from a potential of the form a/r - b/r2	375	(2)
21 The set of orthogonal functions defined by the equation ya" = (x - a)ya	377	(2)
22 Fourier integral expansions	379	(2)
23 Circular integrals	381	(1)
24 Oscillation frequencies of ammonia	382	(3)
25 Spherical functions with spin one	385	(11)
26 Scattering of fast elections: relativistic Born method	396	(6)
27 Frequently used atomic quantities	402	(1)
28 Quasi-stationary states	403	(14)
29 Spherical functions with spin (II)	417	(2)
Volumetto V	419	(50)
1 Representations of the Lorentz group	419	(6)
2 Proton-neutron scattering	425	(2)
3 Zeros of half-order Bessel functions	427	(1)
4 Statistics and thermodynamics	428	(7)
4.1 Entropy of a system in equilibrium	428	(1)
4.2 Perfect gases	429	(1)
4.3 Monoatomic gas	430	(1)
4.4 Diatomic gas	430	(3)
4.5 Numerical expressions for the entropy of a gas	433	(1)
4.6 Free energy of diatomic gases	434	(1)
5 Frequently used polynomials	435	(1)
5.1 Legendre polynomials	435	(1)
6 Spinoy transformations	435	(6)
7 Spherical functions with spin 1/2	441	(5)
8 Infinite-dimensional unitary representations of the Lorentz group	446	(4)
9 The equation (H + λ) A = p	450	(4)
10 Relevant formulas for the atomic eigenfunctions	454	(2)
11 Classical theory of multipole radiation	456	(9)
12 Hydrogen eigenfunctions	465	(4)
Selected facsimile pages	469	(12)
Index	481