The book presents several unique sections and analytical results. For example, the harmonic oscillator calculations are given in diagrammatic form with far greater efficiency in analysis than is posible with wave functions and a treatment is given for the driven harmonic oscillator. The diagrams are forerunners of Feynman diagrams, but at a level of study available to undergraduates. A novel equation for Legendre polynomials is given in the case of the one-electron atom, and an exact N by N determinant equation is solved analytically that has applications in molecular science. The associated equation that appears in the analysis of certain features of many molecules, is needed for the case of a N-state quantum system, and is an example of how the basic idea of difference equations can be of use. Modern biosensor equipment and certain cancer treatments rely upon quanta known as surface plasmons and these are treated in a chapter on applications. Chapters on quantum computing, quantum encryption and quantum entanglement in communication add to the unique contents.