Johnson Charles S. - Problems and Solutions in Quantum Chemistry and Physics
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Problems and Solutions in Quantum Chemistry and Physics: summary, description and annotation
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SUPPLEMENTARY PROBLEMSCHAPTER 7 - HYDROGEN-LIKE ATOMS; PROBLEMS; SUPPLEMENTARY PROBLEMS; CHAPTER 8 - ELECTRONIC STRUCTURE OF ATOMS; PROBLEMS; SUPPLEMENTARY PROBLEMS; CHAPTER 9 - ELECTRONIC STRUCTURE OF MOLECULES; PROBLEMS; SUPPLEMENTARY PROBLEMS; CHAPTER 10 - RADIATION AND MATTER; PROBLEMS; SUPPLEMENTARY PROBLEMS; CHAPTER 11 - MOLECULAR SPECTROSCOPY; PROBLEMS; SUPPLEMENTARY PROBLEMS; CHAPTER 12 - SCATTERING THEORY; PROBLEMS; SUPPLEMENTARY PROBLEMS; APPENDIX 1 - UNITS AND FUNDAMENTAL CONSTANTS; APPENDIX 2 - VECTOR FORMULAS; APPENDIX 3 - HERMITE DIFFERENTIAL EQUATION.
APPENDIX 4 - LEGENDRE POLYNOMIALS AND SPHERICAL HARMONICSAPPENDIX 5 - CURVILINEAR COORDINATES; APPENDIX 6 - TRANSFORMATIONS AND DIAGONALIZATION; APPENDIX 7 - HYDROGENIC WAVE FUNCTIONS AND ENERGIES; APPENDIX 8 - USE OF CHARACTER TABLES; APPENDIX 9 - MAXWELLS EQUATIONS; APPENDIX 10 - USEFUL INTEGRALS; REFERENCES; INDEX. Read more...
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Ref. J. Chem. Ed. , 569 (1971)
The International System of Units (SI) is used in this book. Base units in this system are shown in .
| Physical Quantity | Unit | Symbol |
|---|---|---|
| length | meter | m |
| mass | kilogram | kg |
| time | second | s |
| electric current | ampere | A |
| temperature | kelvin | K |
| amount of substance | mole | mol |
Derived SX units of special interest are shown in .
The Angstrom unit () which is equal to 1010m is often used in atomic calculations. Also the force unit dyne (dyn) equal to 105N and energy unit erg equal to 107J are in common use. Some useful units in terms of physical constants are given in .
| Physical Quantity | Unit | Symbol |
|---|---|---|
| energy | electron volt | eV  1.6021x1019J |
| mass | atomic mass unit | u 1.6604x1027kg |
| electric dipole moment | debye | D 3.3356x1030A  m s |
A selected list of physical constants are shown in
| Constant | Symbol | Value |
|---|---|---|
| speed of light in vacuum | c | 2.997925x108m/s |
| elementary charge | e | 1.602191x1019C |
| Avogadro constant | NA | 6.022169x1023mol1 |
| atomic mass unit | u | 1.660531x1027kg |
| electron rest mass | me | 9.109558x1031kg |
| proton rest mass | mp | 1.672614x1027kg |
| Planck constant | h | 6.626196x1034J.s |
 | 1.054592x1034J s | |
| Rydberg constant | R | 1.097373x107m1 |
| gyromagnetic ratio of proton | p | 2.675196x108rad s1T1 |
| Bohr magneton | B | 9.274096x1024J/T |
| g-factor for free electron | g | 2.0023 |
| gas constant | R | 8.31434 J.K1mol1 |
| Boltzmann constant | kB | 1.38062x1023JK1 |
| fine structure constant | 7.297351x103 | |
| Bohr radius | ao | 5.29167x1011m |
| permittivity of free space | o | 8.854x1012Fm1 |
| 4o | 1.113x1010Fm1 | |
| permeability of free space | o | 4x107NA2 |
Ref., HO,3; SP1,116
We represent the vector 
as follows
where , 
, and 
are unit vectors in the directions of the positive x, y, and z axes as shown below
Dot or Scalar Product:
Cross or Vector Product:
Here is the angle between 
and 
and 
is a unit vector that is perpendicular to the plane containing 
and 
. If a right handed screw is rotated in the direction from 
to 
, the screw will advance in the direction of 
.
Scalar Triple Products:
| 
| = volume of parallelepiped with sides 
, 
, and 
Vector Triple Products:
Differentiation of Vectors:
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