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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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