An excellent treatment of the two-state formalism and its application to almost all the applications mentioned in this article is presented in the third volume of The Feynman Lectures on Physics. The following set of lecture notes covers the necessary mathematics and also treats a few examples in some detail: from the Quantum mechanics II course offered at MIT, http://web.mit.edu/8.05/handouts/Twostates_03.pdf from the same course dealing with neutral particle oscillation, http://web.mit.edu/8.05/handouts/nukaon_07.pdf from the Quantum mechanics I course offered at TIFR, http://theory.tifr.res.in/~sgupta/courses/qm2013/hand4.pdf covers the essential mathematics http://theory.tifr.res.in/~sgupta/courses/qm2013/hand5.pdf ; from the same course deals with the some physical two-state systems and other important aspects of the formalism the mathematical in the initial section is done in a manner similar to these notes http://www.math.columbia.edu/~woit/QM/qubit.pdf, which are from the Quantum Mechanics for Mathematicians course offered at University of Columbia. a book version of the same ; http://www.math.columbia.edu/~woit/QM/qmbook.pdf