APPENDIXES 335

Appendix 1:

Approximate Values of Physical Constants

336 APPENDIXES

Some Astronomical Data

Mass of the Sun

Radius of the Sun

Average Distance between the Earth and the Sun

Average Radius of the Earth

Mass of the Earth

Average Velocity of the Earth in Orbit about the Sun

Average Distance between the Earth and the Moon

Other Commonly Used Units

Angstrom (Å)

Fermi

Barn

Year

Astronomical Year

Parsec

Room Temperature

Horsepower

Calorie

Atmosphere

APPENDIXES

Appendix 2:

337

Conversion Table from Rationalized MKSA to Gaussian Units

Appendix 3:

Vector Identities

338 APPENDIXES

Vector Formulas in Spherical and Cylindrical Coordinates

Spherical Coordinates

Transformation of Coordinates

Transformation of Differentials

Square of the Element of Length

APPENDIXES 339

Transformation of the Coordinates of a Vector

Divergence

Curl

Gradient

APPENDIXES340

Laplacian

Cylindrical Coordinates

Transformation of Coordinates

Transformation of Differentials

Square of the Element of Length

Transformation of the Coordinates of a Vector

APPENDIXES 341

Divergence

Curl

Gradient

Laplacian

Appendix 4:

Legendre Polynomials

342 APPENDIXES

Rodrigues’ Formula

Spherical Harmonics

The first three eigenfunctions of the harmonic oscillator in one dimensionare

Appendix 5:

Harmonic Oscillator

APPENDIXES 343

where is the oscillator frequency.

Appendix 6:

Angular Momentum and Spin

The (Pauli) matrices are

while the vectorThe spin 1 matrices are

344 APPENDIXES

Appendix 7:

Variational Calculations

The general procedure for solving variational problems in one dimensionis to first evaluate three integrals which are functions of the variationalparameter

The two expressions for the kinetic energy K can be shown to be equalby an integration by parts. The second expression is usually easier to use,since one has to take a single derivative of the trial function and thensquare it.

Appendix 8:

Normalized Eigenstates of Hydrogen Atom

APPENDIXES 345

Appendix 9:

Conversion Table for Pressure Units

Appendix 10:

Useful Constants

Resistivity of copper (T = 300 K)

Linear expansion coefficient of copper

Surface tension of water (at 293 K)

Viscosity of water

Heat of vaporization of water (at 373 K, 1 atm)

Velocity of sound in air (at 293 K)

Si band gap

Ge band gap

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