Quantum Mechanics

Review
Kramers began his career in physics in as a graduate student at University of Leiden, but left Leiden in 1916 to do his Ph.D. thesis research with Bohr in Copenhagen. Kramers went to to serve as Bohr's assistant, and later as the vice chairman of Bohr's famous institute for theoretical physics after it was founded in 1921. Kramers eventually returned to his native Holland to continue his academic career, during which he wrote the original German edition of this book, which was first published in 1933. In 1957, the English version of Kramer's QM text was published, translated by Kramers' old graduate student D. ted Haar. As ter Haar's native language was Dutch, he found himself with "the hazardous task of translating from one foreign language to another." Nevertheless, he deemed this to be a worthy undertaking because "I felt that that this book still represents the best available exposition of quantum theory." Although such a bold statement as this might well be challenged, we should be grateful to ter Haar for undertaking this mission and allowing those of us in the English speaking world to get a view of quantum theory from one of Bohr's closest disciples.

Kramers' book is admirable for its direct and unassuming explanation of quantum theory and its mathematical formalism, and written in such as way as not to overwhelm the reader. As stated by Kramers in the preface to his 1933 edition: "The apparent lack of mathematical models which is contritely pointed out in the text is not exclusively due to the incompetence of the author. Physical morals, even (or rather especially) in their purest form, that is, unencumbered by pedagogic afterthoughts, do not live happily together with their mathematical relations in the restricted mansion of the human mind–and neither in the restricted volume of a monograph." Despite these modest qualifications penned by Kramers, his book manages to address the depth of concept and completeness of mathematic description common to graduate level textbooks on QM, including the derivation of the Dirac equation. Like Landau and Lifshitz's QM book, however, Kramers book is still sufficiently unencumbered by abstract arguments that it is accessible to advanced undergraduates. In particular (and also stated in his preface) Kramers avoided reference to group theory in order to make his introduction to QM more approachable.

I should also note that Kramers assembled his book in such a way as to highlight the most important aspects of quantum mechanics–and without bothering to look back at earlier contributions that were considered somewhat dated by 1933. It is particularly noteworthy and laudable that Kramers made no reference to his 1924 work with Bohr and Slater (BKS Theory) that pointed the way to Heisenberg's 1925 work with Born and Jordan on matrix mechanics. Kramers also avoided any mention of his own independent version of the Dirac equation.