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| Morse P., Feshbach H. — Methods of Theoretical Physics (part 2) |
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| Предметный указатель |
Prolate spheroidal coordinates and Laplace equation 1284—1292
Prolate spheroidal coordinates and Laplace equation Green’s function for 1291
Prolate spheroidal coordinates and Laplace equation integral representation of solutions 1288
Prolate spheroidal coordinates and Laplace equation potential of prolate spheroid 1286
Prolate spheroidal coordinates and Laplace equation potential of prolate spheroid in plane 1287
Prolate spheroidal coordinates and Laplace equation potential of spheroid inside sphere 1289
Prolate spheroidal coordinates and Laplace equation uniform field, spheroid in 1286
Prolate spheroidal coordinates and Schroedinger equation for electron in diatomic molecule 646
Prolate spheroidal coordinates and separability 514
Prolate spheroidal coordinates and wave equation, scalar 1502—1511
Prolate spheroidal coordinates and wave equation, scalar Green’s function for 1507
Prolate spheroidal coordinates and wave equation, scalar plane-wave expansion in 1508
Prolate spheroidal coordinates and wave equation, scalar solution in 1502
Prolate spheroidal coordinates and wave equation, vector 1891 1892
Propagation vector 1432
Proper lengths 95
Proper time 93
Pseudoperiodic series 430
Pseudopotential function 14
Pseudovector 209 (see also “Axial vector”)
Q of electromagnetic resonator 1851—1852 1871
Quadrics, confocal and ellipsoidal coordinates 511
Quadrics, confocal and separability 511
Quadripoles, electric 1276
Quadripoles, electric radiation from 1869 1878 1880
quantum mechanics 225—265
Quantum mechanics and central fields see “Central fields in quantum mechanics”
Quantum mechanics and classical mechanics 222 292
Quantum mechanics angular momentum in 1661 1721
Quantum mechanics average values in 232 1639
Quantum mechanics commutation rules 238
Quantum mechanics correspondence principle 250
Quantum mechanics DeBroglie’s relations 225
Quantum mechanics exponential potential in see “Exponential potential in quantum mechanics”
Quantum mechanics free states in 1650 1728
Quantum mechanics independent variables in 233
Quantum mechanics Lorentz invariance in 256
Quantum mechanics many-particle problems in 1719—1745
Quantum mechanics measurement in 231—232
Quantum mechanics momentum space in see “Momentum space in quantum mechanics”
Quantum mechanics operators 78 231
Quantum mechanics Planck’s constant 224
Quantum mechanics Poisson brackets and 230
Quantum mechanics probability in 80 232
Quantum mechanics rotation operators 91
Quantum mechanics Schroedinger equation and 242
Quantum mechanics Schroedinger equation and time-dependent 251
Quantum mechanics time in 251
Quantum mechanics transformation function 236
Quantum mechanics two-particle problems in see “Two-particle problems in quantum mechanics”
Quantum mechanics uncertainty principle 80 88 227
Quantum mechanics variation-iteration in see “Variation-iteration method”
Quantum theory, abstract vector space and 78 231
Quantum theory, abstract vector space and obscrvables in 79
Quantum theory, abstract vector space and rotation operator in 91
Quantum theory, abstract vector space and transformation function in see “Transformation function”
Quantum theory, abstract vector space and uncertainty principle in see “Uncertainty principle”
Quaternion 73 90 104
Quaternion reciprocal 91
Quaternion rotation operator 75
Quaternion tensor 76
Quaternion versor 76
Radial Schroedinger equation 1661
Radial Schroedinger equation for coulomb potential 1663
Radial Schroedinger equation for exponential potential 1670
Radial Schroedinger equation for inverse-cube law of force 1665
Radial Schroedinger equation for oscillator, three-dimensional 1663
Radial Schroedinger equation integral equation for 1072
Radial Schroedinger equation long-wavelength approximation 1088—1092
Radial Schroedinger equation scattering and 1067 1072 1681
Radial Schroedinger equation soluble cases, class of 1670
Radial Schroedinger equation variation-iteration method 1698
Radial Schroedinger equation variational method for energy 1117 1696
Radial Schroedinger equation variational method for phase shift 1123
Radial Schroedinger equation WKBJ methods 1101 (see also “Central fields in quantum mechanics”)
Radiation impedance 899
Radiation of sound from circular boundary 1373
Radiation of sound from dipole source 1479
Radiation of sound from disk, vibrating 1512
Radiation of sound from duct termination 1455 1529
Radiation of sound from many sources 1480
Radiation of sound from piston in sphere 1481
Radiation of sound from sphere 1477
Radiation of sound from strip, vibrating 1423
Radiation of sound in long-wavelength limit 1375 1478
Radiation of sound in short-wavelength limit 1375 1479 1537
Radiation of sound reactance and 1424 1427
Radiation of sound resistance and 1395 1424 1427
Radiation resistance 899 1395 1421 1427
Radiation, electromagnetic from current loop 1881
Radiation, electromagnetic from currents 1875
Radiation, electromagnetic from half-wave antenna 1880
Radiation, electromagnetic from multipoles 1867
Radiation, electromagnetic from multipoles energy of 1880
Radiation, electromagnetic from multipoles for long wavelengths 1877
Radiation, electromagnetic from strip carrying current 1427
Radiative heating 1588
Radius of convergence for Taylor series 376
Radius of convergence for Taylor series and analytic continuation 377 (see also “Circle of convergence”)
Ramsauer effect 1684
Random flight and Green’s function 702
Rayleigh scattering 1884
Rayleigh — Ritz method 1117
Rayleigh — Ritz method and secular determinant 1118
Reactance 300
Reactance and resistance 373 (see also “Impedance”)
Reactance radiation 899 1424 1427
Real and imaginary parts of analytic functions 371
Real and imaginary parts of analytic functions and Hilbert transforms 372
Real and imaginary parts of analytic functions and images 370
Real and imaginary parts of analytic functions and impedances 372
Reciprocal functions 915
Reciprocity principle in abstract vector space 883
Reciprocity principle in abstract vector space and causality 858
Reciprocity principle in abstract vector space for difference equation 701
Reciprocity principle in abstract vector space for diffusion equation 858
Reciprocity principle in abstract vector space for Helmholtz equation 804 808
Reciprocity principle in abstract vector space for Klein — Gordon equation 854
Reciprocity principle in abstract vector space for Laplace equation 799
Reciprocity principle in abstract vector space for scalar wave equation 834
Reciprocity principle in abstract vector space for scattering 1131
Reciprocity principle in abstract vector space for vector wave equation 1769
Reciprocity principle in abstract vector space generalized 872 890
Rectangular coordinates 501 513 656
Rectangular coordinates and wave equation 1364 1434
Rectangular coordinates and wave equation and Green’s function for interior problems 1365 1434
Rectangular coordinates and wave equation and separation of variables 501 513
Rectangular coordinates and wave equation and strip inside rectangular inclosure 1435
Rectangular coordinates and wave equation and vector waves 1773 1823
Rectangular coordinates and wave equation and vector waves and electromagnetic resonators 1849 (see also “Cartesian coordinates”)
Rectangular ducts 1440 1819
Rectangular ducts acoustic transients in 1441
Rectangular ducts constriction in 1443
Rectangular ducts effective impedance for 1447
Rectangular ducts electromagnetic waves in 1819
Rectangular ducts electromagnetic waves in Green’s function for 1823
Rectangular ducts with elbow bend 1448
Recurrence formulas for Bessel functions 619 1322
Recurrence formulas for Bessel functions spherical 622 1574
Recurrence formulas for confluent hypergeometric functions 671
Recurrence formulas for gamma functions 419
Recurrence formulas for Gegenbauer polynomials 782
Recurrence formulas for Hermite polynomials 786
Recurrence formulas for hypergeometric functions 668
Recurrence formulas for Jacobi polynomials 1755
Recurrence formulas for Laguerre polynomials 784
Recurrence formulas for Legendre functions 735 782 1325
Recurrence formulas for Legendre polynomials 600 749 782 1326
Recurrence formulas for polygamma functions 423
Recurrence formulas for semicylindrical functions 1756
| Recurrence formulas for spherical harmonics, complex 1062
Recurrence formulas for Weber functions 1566
Recursion formulas and differential equations 539 568
Recursion formulas and differential equations and difference equation 540
Recursion formulas and differential equations three-term 555 557
Recursion formulas and differential equations two-term 542 570
Reflection coefficient 130 1066 1071 1489
Reflection coefficient Born approximation for 1081
Reflection coefficient Fredholm series for 1081
Reflection coefficient WKBJ approximation for 1100
Reflection, diffuse 1619
Reflection, diffuse for Schroedinger equation 1071 1075 1094 1655 1060
Reflection, diffuse for sound waves in ducts 1443
Reflection, diffuse for sound waves in ducts lined 1522
Reflection, diffuse for sound waves in ducts with constriction 1443
Reflection, diffuse for sound waves in ducts with elbow bend 1447
Reflection, diffuse for sound waves in ducts with iris diaphragm 1514
Reflection, diffuse for sound waves in ducts with termination 1529
Reflection, diffuse of elastic wave 1814 1818
Reflection, diffuse of electromagnetic wave, from end of duct 1832
Reflection, diffuse of electromagnetic wave, from plane 1813
Reflection, diffuse of electromagnetic wave, from strip 1427
Reflection, diffuse of electromagnetic wave, from wire across duct 1838
Reflection, diffuse Schwarz 393
Reflection, diffuse variational principle for 1128 1517
Refraction, index of 1815
Refraction, index of and Snell’s law 1817
Region, multiply connected 363
Regular singular points 532
Regular singular points and indicial equation 534
Regular singular points differential equation, table of formulas 671—673
Regular singular points differential equation, with one 536 667
Regular singular points differential equation, with one and one irregular 550—555
Regular singular points differential equation, with one and one irregular and Bessel equation 553
Regular singular points differential equation, with one and one irregular and confluent hypergeometric function 552
Regular singular points differential equation, with one and one irregular and coulomb wave function 550 553
Regular singular points differential equation, with three 537—549
Regular singular points differential equation, with three and hypergeometric functions 541
Regular singular points differential equation, with three and Pappentz equation 539
Regular singular points differential equation, with three standard form 539
Regular singular points differential equation, with three table of formulas 667—671
Regular singular points differential equation, with two 536 671
Regular singular points differential equation, with two and one irregular 555
Regular singular points differential equation, with two and one irregular and Mathicu’s equation 556
Relativistic energy 97
Relativistic particle, Lagrange function for 297
Relativity see “Lorentz transformation”
Relaxation oscillations and conductivity 208
Reproduction rate 1596
Residues 408 481
Residues calculus of 408—419
Resistance 300
Resistance and reactance 373 (see also “Impedance”)
Resistance flow 1198
Resistance radiation 899 1395 1424 1427
Resonance effects in scattering 1392 1490 1684
Resonant frequencies 287
Resonant frequencies variational principle for 1112 (see also “Eigenvalues”; “Resonators”)
Resonators, acoustic, cylindrical with slot 1392
Resonators, acoustic, Helmholtz 1490
Resonators, acoustic, rectangular room with strip 1435
Resonators, acoustic, sphere 1468
Resonators, acoustic, sphere vibrating string in 1472
Resonators, acoustic, sphere with hole 1490
Resonators, electromagnetic 1849
Resonators, electromagnetic energy loss in 1851 1871
Resonators, electromagnetic excitation by current 1853
Resonators, electromagnetic excitation by wave guide 1855
Resonators, electromagnetic Green’s function for 1850
Resonators, electromagnetic klystron 1859
Resonators, electromagnetic Q of 1851 1871
Resonators, electromagnetic rectangular parallelepiped 1849
Resonators, electromagnetic spherical cavity 1870
Resonators, electromagnetic spherical cavity containing small object 1887
Resonators, electromagnetic spherical cavity variational method for 1895
Retarded potential 206 840 873
Reynolds number 1795
Riemann surfaces 401
Right-handed coordinate system 9 23
Robertson condition and separability 510
Rotation operator 33
Rotation operator in quantum theory 91
Rotation operator of spinors 102
Rotation operator quaternion 75
Rotation operator rigid 61
Rotation operator spinor 105
Rotational coordinates and separability 646
Rutherford scattering 1669 1691
Saddle point 440 (see also “Steepest descents method
Saloon and random flight 702
scalar 46 55
Scalar fields 4
Scalar fields general properties 302—318
Scalar fields table 343—345
Scalar fields variational principle 302—318
Scalar potential 53 144 1763
Scalar potential wave equation for 206
Scalar product of vectors 10
Scalar waves see “Wave equation scalar”
Scale factors 24 504
Scale factors and concentration points 504
Scattering amplitude 1065 1069 1070 1167
Scattering amplitude integral equation for 1077
Scattering amplitude variational principle for 1131 1135 1168 1701 1704
Scattering of by cylinder 1376
Scattering of by cylinder and effective width 1379
Scattering of by cylinder long-wavelength limit 1380
Scattering of by cylinder shadow 1380
Scattering of by cylinder short-wavelength limit 1380
Scattering of by cylinder with slit 1387
Scattering of by disk 1522
Scattering of by ensemble 1494
Scattering of by Helmholtz resonator 1490
Scattering of by parabolic boundaries 1402
Scattering of by sphere 1483
Scattering of by sphere short-wavelength limit 1485 1551
Scattering of by sphere with complex index of refraction 1486
Scattering of by sphere with impedance boundary condition 1489
Scattering of by strips 1428 1549
Scattering of coherent 1496
Scattering of incoherent 1496
Scattering of slow particles 1686
Scattering of sound, by air bubbles in water 1498
Scattering of variational principle for 1544
Scattering, Born approximation for 1073 1076 1688 1692 1738
Scattering, boundary conditions for 1065
Scattering, cross-section 178 1066 1545 1883
Scattering, cross-section and forward scattering 1069 1547
Scattering, cross-section differential 1066
Scattering, dyadic 1897
Scattering, for Schroedinger equation 1681
Scattering, for Schroedinger equation elastic and inelastic scattering 1740
Scattering, for Schroedinger equation form factor and 1691 1742
Scattering, for Schroedinger equation particle exchange in 1742
Scattering, for Schroedinger equation Rutherford 1669 1691
Scattering, for Schroedinger equation two-body problem in 1738
Scattering, for Schroedinger equation variation-iteration method 1704
Scattering, for Schroedinger equation variational method for 1123 1130 1135 1160 1168 1701 1704
Scattering, forward, distribution function for 1610 1748 1750
Scattering, Fredholm series for 1078
Scattering, from central fields 1681
Scattering, from central fields Born approximation for 1073 1688
Scattering, from central fields exponential potential for 1687 1695 1702
Scattering, from central fields long-wavelength approximation 1088 1686
Scattering, from central fields of shielded atom 1682
Scattering, from central fields phase shifts and 1068 1072 1681
Scattering, from central fields Ramsauer effects for 1684
Scattering, from central fields resonance effects for 1684
Scattering, from central fields variation-iteration method for 1704
Scattering, from central fields variational method for 1123 1130 1160 1701 1704
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