A
AN system, 1 7 2 - 1 7 5
Α Α Ά " ··· systems, 3 6 5 - 3 7 3 , 3 8 9 A B system, 1 8 9 - 1 9 6
2- b r o m o- 5- c h l o r o t h i o p h e n e , 1 9 6 d o u b l e q u a n t u m transition, 4 1 2 - 4 1 3 eigenvalues a n d eigenvectors, 1 9 0 frequencies a n d intensities, 1 9 2 h a m i l t o n i a n m a t r i x , 1 8 9
m o d u l a t i o n of echo envelope, 4 4 2 - 4 4 5 s p e c t r u m , 1 9 1 - 1 9 6
theoretical spectra, 1 9 4 A2B system, 1 9 6 - 2 0 8
— C H2O H p r o t o n s in benzyl alcohol, 2 0 3 - 2 0 4 , 2 0 6
eigenvalues a n d eigenvectors, 1 9 8 frequencies a n d intensities, 2 0 5 h a m i l t o n i a n m a t r i x , 1 9 7 - 1 9 8 irreducible c o m p o n e n t s , 1 9 9 , 2 0 2 m u l t i p l e q u a n t u m transitions, 4 1 3 - 4 1 6 s p e c t r u m , 1 9 9 , 2 0 1
theoretical spectra, 2 0 0 - 2 0 2 1, 2 , 3- t r i c h l o r o b e n z e n e , 2 0 2 A3B system, 2 1 6 - 2 2 4
frequencies a n d intensities, 2 1 8 - 2 1 9 h a m i l t o n i a n m a t r i x , 2 1 0
irreducible c o m p o n e n t s , 2 1 7 m e t h y l m e r c a p t a n , 2 2 4 theoretical spectra, 2 2 0 - 2 2 1 transition d i a g r a m s , 2 2 4 A4B system, 2 2 4 - 2 2 8
frequencies a n d intensities, 2 2 2 - 2 2 3 irreducible c o m p o n e n t s , 2 2 7
theoretical spectra, 2 2 5 - 2 2 6 transition d i a g r a m s , 2 2 7 A „A Β s y s t e m , 2 0 8 - 2 1 6
eigenvalues a n d eigenvectors, 2 1 1 frequencies a n d intensities, 2 1 5 general p r o p e r t i e s , 2 2 9 - 2 3 0 h a m i l t o n i a n m a t r i x , 2 0 8 - 2 1 1 n u m b e r of resonances, 2 1 6 s p e c t r u m , 2 1 3 - 2 1 6 A2B2 system, 2 3 5 - 2 4 1
ethylene m o n o t h i o c a r b o n a t e , 2 4 1 frequencies a n d intensities, 2 3 6 i r r e d u c i b l e c o m p o n e n t s , 2 3 8 theoretical spectra, 2 3 9 - 2 4 0 transition d i a g r a m s , 2 3 7 A3B2 system, 2 4 1 - 2 5 0
ethyl iodide, 2 5 0
frequencies a n d intensities, 2 4 2 - 2 4 5 i r r e d u c i b l e c o m p o n e n t s , 2 4 6 theoretical spectra, 2 4 7 - 2 4 8 transition d i a g r a m s , 2 4 9 A6B2 system
irreducible c o m p o n e n t s , 1 8 2 AnBn system
s y m m e t r y t h e o r e m , 2 5 4 - 2 5 5 Aw A Bn D system
general p r o p e r t i e s , 2 3 5 , 2 5 0 - 2 5 4 Α „ΑΒ2 system
theory, 2 3 0 - 2 3 5 A X system
d o u b l e r e s o n a n c e s p e c t r u m , 4 2 9 A JAX1 /2 system
d o u b l e r e s o n a n c e s p e c t r u m , 4 2 8 5 4 2
A JAXx s y s t e m
d o u b l e resonance s p e c t r u m , 4 2 8
AlA X3 / 2 s y s t e m
d o u b l e r e s o n a n c e s p e c t r u m , 428
A NAX nx sys t e m> 136-137, 298 d o u b l e resonance s p e c t r u m , 4 2 3 - 4 3 3 A B C system
2 - b r o m o t h i o p h e n e , 279 2 - c h l o r o t h i o p h e n e , 280 frequencies a n d intensities, 272 general p r o p e r t i e s , 2 7 8 , 2 8 2 - 2 8 3 h a m i l t o n i a n m a t r i x , 271 2 - i o d o t h i o p h e n e , 281
s t r o n g coupling, 274, 2 7 6 - 2 7 8 vinyl acetate, 275
weak coupling, 2 7 3 - 2 7 4 A B X system, 299, 3 0 1 - 3 0 5
2-fluoro-4, 6 - d i c h l o r o p h e n o l , 304 frequencies a n d intensities, 301
m u l t i p l e q u a n t u m transitions, 4 1 7 - 4 1 8 transition d i a g r a m , 287
A B X2 system, 305, 3 0 6 - 3 0 7
A B XN system, 2 9 8 - 2 9 9 frequencies a n d intensities, 300 Α2Β Χη χ system, 305, 308-311
frequencies a n d intensities, 3 0 8 - 3 1 0 Αη ΑΒ Χη χ s y s t e m
eigenvalues a n d eigenvectors, 293 frequencies a n d intensities, 2 9 4 - 2 9 5 h a m i l t o n i a n m a t r i x , 2 9 0 - 2 9 1 n u m b e r of resonances, 2 9 4 - 2 9 5 signs of c o u p l i n g constants, 2 9 6 - 2 9 8 s p e c t r u m , 292, 296
A B2C system, 258
A5B3C2 system, 182
A A ' B B' system, 3 7 6 - 3 8 2
eigenvalues a n d eigenvectors, 379 frequencies a n d intensities, 380 h a m i l t o n i a n m a t r i x , 377 p r o p e r t i e s of, 3 7 8 - 3 7 9 , 3 8 1 - 3 8 2 special cases, 3 8 2 - 3 8 4
A A ' · · · B B ' · · · C C ··· systems, 3 7 3 - 3 7 6
A A ' X X' s y s t e m , 3 8 3 - 3 8 4 , 3 8 9 - 3 9 0 , 3 9 5 - 398
d e c o m p o s i t i o n of h a m i l t o n i a n m a t r i x , 3 9 8 frequencies a n d intensities, 384
A2A2' B B ' system, 3 8 5 - 3 8 6
r e d u c t i o n i n t o irreducible c o m p o n e n t s , 386
A3A3' B B ' system, 3 8 5 - 3 8 7
r e d u c t i o n into irreducible c o m p o n e n t s , 385
A A ' A " X X ' X " system, 3 8 9 - 3 9 0 , 395, 3 9 9 - 403
d e c o m p o s i t i o n of h a m i l t o n i a n m a t r i x , 4 0 3 A3A3' A3" B B ' B " system
r e d u c t i o n into irreducible c o m p o n e n t s , 386
Α Α Ά ' Ά " ' X X ' system, 3 8 9 - 3 9 0 , 3 9 5 - 3 9 6 , 3 9 8 - 3 9 9
d e c o m p o s i t i o n of h a m i l t o n i a n m a t r i x , 4 0 0 A n g u l a r m o m e n t u m , see also spin o p e r a t o r s addition of angular m o m e n t a , 107-125 classical, 1-5
c o m m u t a t i o n relations, 5 0 - 5 3 , 105, 108 eigenvalues, 56, 6 0 - 6 2 , 115-125 eigenvectors, 52, 53, 6 0 - 6 2 , 109, 114-125 invariance of, 5 1 - 5 2
of m u l t i s p i n systems, 9 5 - 1 2 5 orbital, 3
q u a n t i z a t i o n , 4
q u a n t u m mechanical, 4 8 - 7 4 , 105-125 of spin 1/2 particles, 114-122 spin o p e r a t o r s , 4 8 - 4 9 transformation, 4 9 - 5 0
t r a n s f o r m e d eigenvectors, 6 8 - 7 4 total, 107-108
vector character, 4 8 - 5 0 Axis of q u a n t i z a t i o n , 4
Β
Binomial coefficient, 448 Bloch e q u a t i o n , 3 9 - 4 5
steady-state solution, 41 transient oscillations, 44, 45 transient solution, 40 u m o d e , 4 2
ν m o d e , 42 B o h r m a g n e t o n
electron, 5 nuclear, 14
B o l t z m a n n d i s t r i b u t i o n , 33 m a t r i x , 4 3 9 - 4 4 0
C
C h a r a c t e r , 349
C h a r a c t e r tables, 3 5 4 - 3 5 5 Class, 336
C o m m u t a t o r , 447
C o n s t a n t s of the m o t i o n , 2, 79-81 a p p r o x i m a t e , 2 8 3 - 2 8 6
coupled systems, 146-149 s y m m e t r y , 329, 347, 363 Coset, 335
C o u p l i n g constant, see s p i n - s p i n c o u p l i n g constant
D
D e t e r m i n a n t a l e q u a t i o n , 4 6 5 - 4 6 6 D i a m a g n e t i s m , 32
Difference e q u a t i o n of Laplace, 4 8 6 - 4 8 8 D i r a c notation, 4 7 0 - 4 7 1
D i r e c t p r o d u c t g r o u p s , 3 9 1 - 3 9 5 D i r e c t s u m , 3 5 1 , 463
D o u b l e resonance, 4 1 8 - 4 3 7 of Α ΗΑΧΗΧ systems, 4 2 3 - 4 3 4 d e c o u p l i n g by, 4 1 8 - 4 1 9 , 427, 429 field s w e e p , 4 2 3 , 4 3 1 , 433 frequency sweep, 423
tickling e x p e r i m e n t s , 420, 4 3 5 - 4 3 7 D u a l space, 453
Ε Electron spin, 6-8 E n e r g y r e p r e s e n t a t i o n , 78 E u l e r angles, 4 7 8 - 4 7 9 E x p e c t a t i o n value, 79 E x p o n e n t i a l operators,
definition, 480 expansion, 4 8 3 - 4 8 5 properties, 4 8 0 - 4 8 2
F F r e e i n d u c t i o n decay, 438
G G r o u p
abelian, 330 abstract, 330 axioms, 330
conjugate elements, 336 h o m o m o r p h i c , 333 identity, 330 inverse, 330 i s o m o r p h i c , 333
of magnetically equivalent nuclei, 137, 175-178
multiplication table, 3 3 1 - 3 3 2 order, 331
of symmetrically equivalent nuclei, 341 G r o u p characters, 349
G r o u p element, 330 order, 334
G r o u p r e p r e s e n t a t i o n s d i m e n s i o n s , 353 equivalent, 345, 348 faithful, 344, 348 irreducible, 3 5 2 - 3 5 3 by linear operators, 3 4 3 - 3 4 7 by matrices, 3 4 7 - 3 5 8 n o n e q u i v a l e n t , 348 orthogonality relations, 353 reducible, 351
r e d u c t i o n , 3 5 6 - 3 5 8 unfaithful, 344, 348 b y u n i t a r y matrices, 348 G y r o m a g n e t i c ratio, 5
electron, 7 nuclear, 15 p r o t o n , 15
H
H a m i l t o n i a n matrix, 75, 149-156 elements, 152-156
for magnetically equivalent g r o u p s , 179—
183
s t r u c t u r e in coupled systems, 149-151 H a m i l t o n i a n operator
for coupled systems, 143-146
in d o u b l e resonance of coupled systems, 420-421
in rotating fields, 89, 156 in stationary fields, 81 s y m m e t r y g r o u p , 345
transformation of in d o u b l e resonance, 4 2 1 - 4 2 3
for t w o - g r o u p systems, 187 H e i s e n b e r g coordinate system, 78 H e i s e n b e r g e q u a t i o n s , 8 6 - 8 8
for coupled systems, 148-149 H e r m i t i a n matrix, 468
diagonalization, 468 eigenvalues, 468 H o m o m o r p h i s m , 333
ι
I d e n t i t y o p e r a t o r , 4 5 6 I d e n t i t y r e p r e s e n t a t i o n , 344 I n t e n s i t y t h e o r e m s , 1 6 9 - 1 7 2 , 183 I n v a r i a n t g r o u p (of nuclei), 341 I r r e d u c i b l e c o m p o n e n t s , 1 8 0 - 1 8 6
intensities, 1 8 3 - 1 8 4 s u p e r p o s i t i o n principle, 181 I s o m o r p h i s m , 333
Κ K r o n e c k e r delta, 447
K r o n e c k e r p r o d u c t s of linear t r a n s f o r m a - tions, see also linear t r a n s f o r m a t i o n s , 9 8 - 1 0 1
adjoint, 100
of a n g u l a r m o m e n t u m o p e r a t o r s , 1 0 5 - 107
c o m m u t a t i o n p r o p e r t i e s , 99, 100 d e t e r m i n a n t s , 104
diagonalization, 1 0 4 - 1 0 5 inverse, 100
m a t r i x r e p r e s e n t a t i o n s , 1 0 1 - 1 0 4 trace, 104
L L a r m o r precession, 18
L i n e a r t r a n s f o r m a t i o n s , see also o p e r a t o r s , 4 5 6 - 4 6 2
adjoints, 4 6 0 - 4 6 1 c o m m u t a t o r , 457 c o m m u t i n g , 4 5 7
K r o n e c k e r p r o d u c t s , 9 5 - 1 0 1 m a t r i x r e p r e s e n t a t i o n s , 4 5 8 - 4 6 0 n o n s i n g u l a r , 4 5 7
o r t h o g o n a l , 4 7 2 - 4 7 9 p r o d u c t s , 4 5 6 singular, 457 L i n e w i d t h s , 3 6 - 3 9
M
M a g n e t i c equivalence, 175-179 conditions for, 177
M a g n e t i c field adiabatic c h a n g e , 22 effective, 25 oscillating, 2 8 , 29
p e r t u r b i n g , 418 rotating, 2 2 s t i m u l a t i n g , 4 1 8 M a g n e t i c flux, 35 M a g n e t i c m o m e n t
classical d y n a m i c s , 1 6 - 2 2 , 2 9 - 3 2 orbital, 5
n e u t r o n , 14 p r o t o n , 1 4 - 1 6
q u a n t u m d y n a m i c s , 7 5 - 9 4 r o t a t i n g fields, 2 1 - 2 2 , 8 9 - 9 4 in stationary fields, 17, 8 1 - 8 6 M a g n e t i c susceptibility, 32, 35 M a g n e t i z a t i o n , 32
saturation, 34 static, 33 M a g n e t o n
Bohr, 5 nuclear Bohr, 14
M a j o r a n a formula, 9 2 - 9 4 , 4 0 7 M a t r i c e s
diagonalization, 4 6 4 - 4 6 8 direct s u m , 463
eigenvalues, 4 6 4 eigenvectors, 4 6 4 h e r m i t i a n , 4 4 8 , 4 6 8 invariants, 4 6 2 - 4 6 3 inverse, 461 n o n s i n g u l a r , 4 4 8 , 4 5 7 o r t h o g o n a l , 4 7 2 - 4 7 9 S c h u r canonical form, 4 6 4 singular, 4 4 8 , 457
s k e w - h e r m i t i a n , 448 s k e w - s y m m e t r i c , 448 s y m m e t r i c , 4 4 8 t r a n s p o s e , 4 4 7 triangular, 4 6 4 u n i t a r y , 4 4 8 , 4 6 6 - 4 6 8 M o m e n t analysis, 3 1 2 - 3 2 8
a p p r o x i m a t e calculations, 326
calculation of spectral m o m e n t s , 3 1 4 - 3 1 7 definition of spectral m o m e n t s , 313 i m a g i n a r y solutions, 3 2 4 - 3 2 6 m o m e n t s of c o m p l e t e s y s t e m , 317 m o m e n t s of irreducible c o m p o n e n t s , 316 m u l t i p l e solutions, 3 1 9 - 3 2 0 , 325 t h r e e - g r o u p systems, 3 1 9 - 3 2 6 t w o - g r o u p systems, 3 1 7 - 3 1 8
M u l t i p l e q u a n t u m transitions, 27, 9 2 - 9 4 , 174, 4 0 6 - 4 1 7
A B system, 4 1 2 - 4 1 3 A2B system, 4 1 3 - 4 1 6 A B X system, 417 frequencies, 408 theory, 4 0 9 - 4 1 2
Ν
N u c l e a r m o m e n t , 14-16 N u c l e a r spin, 12-14
Ο
O c t a h e d r a l g r o u p , 340 full, 340
O p e r a t o r , see also linear t r a n s f o r m a t i o n , spin o p e r a t o r s
exponential, 480 h e r m i t i a n , 448, 462 i d e m p o t e n t , 358 inverse, 457 n o r m a l , 4 6 1 - 4 6 2 o r t h o g o n a l , 462, 4 7 2 - 4 7 9 projection, 358
q u a n t u m mechanical m e a n value, 79 q u a n t u m m e c h a n i c a l t i m e derivative, 80 spin inversion, 154-156
s y m m e t r i c , 462 unitary, 462, 4 6 6 - 4 6 8 vector, 4 8 - 5 0
O r t h o g o n a l t r a n s f o r m a t i o n , 4 7 2 - 4 7 9 i m p r o p e r , 473
p r o p e r , 473
Ρ
P a r a m a g n e t i s m , 32 nuclear, 3 2 - 3 4
P e r t u r b a t i o n expansions, 2 5 9 - 2 6 0 P e r t u r b a t i o n theory, 2 5 9 - 2 8 3
first-order spectra for s t r o n g c o u p l i n g , 2 6 8 - 2 6 9
first-order spectra for weak coupling, 2 6 6 - 2 6 9
p e r t u r b a t i o n o p e r a t o r , 259
s e c o n d - o r d e r spectra for weak coupling, 2 6 9 - 2 7 0
s t r o n g coupling, 2 6 1 , 2 6 2 - 2 6 4 s y m m e t r i c a l systems, 3 8 8 - 4 0 3 weak c o u p l i n g systems, 2 6 1 - 2 6 2
z e r o - o r d e r h a m i l t o n i a n , 259
z e r o - o r d e r strongly c o u p l e d systems, 265 z e r o - o r d e r weakly c o u p l e d systems, 265 P h e n o m e n o l o g i c a l theory, 3 2 - 4 5
Probability a m p l i t u d e , 90, 158-160 P r o d u c t basis, 97
P r o d u c t spaces, 9 5 - 9 8 definition of, 9 6 - 9 7 d i m e n s i o n s of, 98 Projection o p e r a t o r s , 358
for <6\,%2Ν ^ 3 , 364 c o n s t r u c t i o n , 3 6 1 - 3 6 5 eigenvalues, 359 K r o n e c k e r p r o d u c t s , 395 m u t u a l orthogonality, 3 6 1 , 363 nullity, 359
rank, 359
Q
Q u a d r u p o l e m o m e n t , 16, 144
R
Relaxation t i m e s , 3 6 - 3 9 t h e r m a l , 37
transverse, 38
R e s o n a n c e p h e n o m e n a , 2 3 - 3 2 algebraic analysis, 2 9 - 3 2
classical description, 2 4 - 2 7 , 2 9 - 3 2 q u a n t u m m e c h a n i c a l description, 2 7 - 2 8 R o t a t i n g c o o r d i n a t e system, 2 3 - 2 4 , 40 Rotation
w-dimensional, 473 t h r e e - d i m e n s i o n a l , 4 7 3 - 4 7 9 Rotation o p e r a t o r , 6 5 - 6 7 , 474, 483
in t e r m s of direction cosines, 477 in t e r m s of E u l e r angles, 67, 68, 479 Rotational invariance, 142, 345
S
Scalar o p e r a t o r , 456 Scalar p r o d u c t , 4 5 4 - 4 5 6
h e r m i t i a n , 455
S c h r ö d i n g e r e q u a t i o n , 7 5 - 7 7 integration, 7 7 - 7 9 m a t r i x representation, 76 operational solution, 79 Secular e q u a t i o n , 4 6 5 - 4 6 6
Selection rules, 150, 1 6 0 - 1 6 1 , 178, 180, 181 s y m m e t r i c a l systems, 3 6 3 - 3 6 4
S h i e l d i n g constant, 128 Shielding tensor, 129 Shifts, 127-135
a t o m i c , 127 chemical, 130 intermolecular, 130 intramolecular, 132 molecular, 129
Signal intensities, 164-167 relative, 166-167
total intensity t h e o r e m , 169-172 Similarity t r a n s f o r m a t i o n s , 4 6 2 - 4 6 3
invariants, 4 6 2 - 4 6 3 Spin, 7, 62
electron, 6 - 8 n e u t r o n , 13 nuclear, 12-14 p r o t o n , 12 vector, 48
S p i n echo e x p e r i m e n t s , 4 1 , 4 3 7 - 4 4 5 m o d u l a t i o n of echo a m p l i t u d e , 439, 442,
445
S p i n inversion o p e r a t o r , 154-156 S p i n multiplicity, 6 1 , 109, 120-125 S p i n multiplicity index, 6 1 , 110 S p i n o p e r a t o r s , 4 8 - 5 2 , 105-108
cartesian c o m p o n e n t s , 48
c o m m u t a t i o n rules, 5 0 - 5 3 , 105, 108 eigenvalues, 56, 6 0 - 6 2 , 115-125 eigenvectors, 5 2 - 5 3 , 6 0 - 6 2 , 109, 114-125 linear i n d e p e n d e n c e of, 490
m a t r i x r e p r e s e n t a t i o n , 5 7 - 6 0 Pauli, 5 9 - 6 0
total, 107-108
t r a n s f o r m a t i o n , 49, 50, 6 4 - 6 7 t r a n s f o r m e d eigenvectors, 6 8 - 7 4 S p i n q u a n t u m n u m b e r , 7, 13, 56, 6 1 , 109,
114
m u l t i s p i n systems, 114, 120, 125 S p i n rotation operator, 6 5 - 6 8
E u l e r d e c o m p o s i t i o n of, 67 S p i n space, 6 2 - 6 4
d i m e n s i o n , 63, 98
S p i n - s p i n c o u p l i n g c o n s t a n t , 136-139, 141 bilinear, 139
t h e o r e m on absolute signs, 1 6 7 - 1 6 9 S p i n - s p i n interactions, 135-143
bilinear, 139
multilinear, 142-143
rotational invariance, 136, 142 Spin states, 6 2 - 6 4 , 95, 96 S p i n system, see specific type S p i n variable, 7, 13, 56
degeneracy, 6 0 - 6 2 , 111, 113 total, 111-113
S p i n vector, 48 State vector, 75
d u a l , 76
S t e a d y - s t a t e e x p e r i m e n t s , 41 S t e r e o g r a p h i c projection, 20
a n d q u a n t i z a t i o n , 88
S t e r n - G e r l a c h e x p e r i m e n t , 8-12 S u b g r o u p , 334
cyclic, 334 i m p r o p e r , 334 p r o p e r , 334 S u b s p a c e , 4 5 0 - 4 5 1
S y m m e t r i c a l l y e q u i v a l e n t g r o u p s (of nuclei), 341
S y m m e t r i c a l l y equivalent nuclei, 341 S y m m e t r i z a t i o n of basis vectors, 3 5 8 - 3 7 6 S y m m e t r i z a t i o n of the p r o d u c t basis, 3 9 6 -
403 S y m m e t r y , 337 S y m m e t r y axis principal, 338 secondary, 338 S y m m e t r y conditions, 343 S y m m e t r y g r o u p s , 337-341
d i h e d r a l , 339 f o u r - g r o u p , 332, 339 molecular, 342
of irreducible c o m p o n e n t s , 3 8 7 - 3 8 8
V> nn , 340
Vn v, 340
tfoo , 341 tfoo* , 341
^ 3 , 3 3 8 - 3 3 9 , 3 4 9 - 3 5 3 , 355, 358
®n , 339
•Vnk , 340
®2 , 340, 3 4 9 - 3 5 0
^οο
Λ,
3410, 340
Θη , 340 03 , 340
Θζ+ , 341 02 , 341
<V,
341^ , 340
^ , 340
S y m m e t r y p l a n e s , 338 S y m m e t r y species, 353
Τ T e t r a h e d r a l g r o u p , 340
full, 340
T h r e e - d i m e n s i o n a l o r t h o g o n a l t r a n s - formations, 4 7 3 - 4 7 9
T h r e e - d i m e n s i o n a l p u r e rotation g r o u p , 341
T h r e e - d i m e n s i o n a l rotation g r o u p , 340 s u b g r o u p s , 341
a n d t h e t h e o r y of angular m o m e n t u m , 4 0 3 - 4 0 4
T r a c e
définition, 463 invariance, 463
of a K r o n e c k e r p r o d u c t , 105 of spin o p e r a t o r s , 4 8 9 - 4 9 2 T r a n s i t i o n
classification, 188 c o n n e c t e d , 436 m i x e d , 188
m u l t i p l e q u a n t u m , 27, 4 0 6 - 4 1 7 probability, 9 0 - 9 2 , 156-164 progressive, 4 3 6
rate, 163 regressive, 436 T r a n s i t i o n d i a g r a m , 208
T r a n s i t i o n probability, 9 0 - 9 2 , 156-164 T w o - d i m e n s i o n a l p u r e rotation g r o u p , 341 T w o - d i m e n s i o n a l rotation g r o u p , 341
U U n i t a r y m a t r i x
diagonalization, 466-468
eigenvalues, 468
i n d e p e n d e n t p a r a m e t e r s , 467 U n i t a r y space, 455
V Vectors
addition, 448 c o m p o n e n t s , 453 dual, 4 5 3 - 4 5 4
linear c o m b i n a t i o n s , 4 5 0 linearly d e p e n d e n t , 451 linearly i n d e p e n d e n t , 451 rc-tuples, 449
o r t h o g o n a l , 455 o r t h o n o r m a l , 455
scalar multiplication of, 449 scalar p r o d u c t , 454
Vector o p e r a t o r , 4 8 - 5 0
Vector spaces, see also p r o d u c t spaces, 448 basis, 452
d i m e n s i o n , 452 unitary, 455
W Wiggles, 45
X X - a p p r o x i m a t i o n , 2 8 3 - 2 9 0
effective chemical shifts, 2 8 9 - 2 9 0 intensity t h e o r e m s , 2 8 8 - 2 8 9 selection rules, 2 8 6 - 2 8 8 s y m m e t r i c a l systems, 388-391
Ζ Z e r o operator, 456
