Applied Quantum Mechanics, Second Edition
Using real-world engineering examples to engage the reader, the author of this detailed text makes quantum mechanics accessible and relevant to the engineering student.
TABLE OF CONTENTS Applied Quantum Mechanics, Second Edition
Appendix E: Vector Calculus and Maxwell s Equations
E.1 Vector Calculus
Cartesian coordinates (x, y, z)
where x ~, y ~ and z ~ are unit vectors in the x, y, and z directions respectively.
Spherical coordinates ( r, ?, 
)
where we note that the first term on the right-hand side
Useful vector relationships for the vector fields a , b, and c are
Other useful relations in vector calculus are the divergence theorem relating volume and surface integrals
where n ~ is the unit-normal vector to the surface S. Stokes s theorem relates surface and line integrals
where d l is the vector line element on the closed loop C.
E.2 Maxwell s Equations
In SI-MKS units
| ? D = ? | Coulomb s law. |
| ? B = 0 | No magnetic monopoles. |
| | Faraday s law. |
| | Modified Ampere s law. |
Current continuity requires that 
and in these equations for linear media B= H and D = ? E = ? 0(1 + ? e) E = ? 0 E + P.
In SI units, the permittivity of free space is ? 0 = 8 .854 187 8 10 ? 12 Fm ? 1 exactly, and the permeability of free space is 0 = 4 ? 10 ? 7 Hm ? 1.
In Gaussian or CGS units, Maxwell s equations take on...
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