By Philip L. Taylor
This reader-friendly advent to the speculation that underlies the various attention-grabbing houses of solids assumes merely an common wisdom of quantum mechanics. Taylor and Heinonen describe the tools for appearing calculations and making predictions of a few of the numerous complicated phenomena that ensue in solids and quantum drinks. Their booklet, aimed toward complex undergraduates and starting graduate scholars, leads the reader from the basic habit of electrons and atoms in solids to the main lately explored manifestations of the quantum nature of condensed subject.
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Extra resources for A quantum approach to condensed matter physics
S by Eq. 41) implies that each bundle structure of duces a translation of t E T, we denote by T
24 INTRODUCTION c3 with the scalar product space of holomorphic functions on given by the right hand side of the above equation. As in the case of the Schrodinger representation. the components of the position. the momentum. and the angular momentum vectors preserve the polarization. ,. 1 ® \1- /;;z \1_ /;;z to denote the quantization ~B in the Bargmann-Fock representation. ll.... z. •• It should be noted that the ground state energy is due to the transformation properties of the bundle under the one-parameter group of canonical transformations generated by H.
Ment is valid for any dynamical variable The same argu- f. The Blattner-Kostant-Sternberg construction leads to a linear isomorphism ~ between ~ and the Bargmann-Fock representation space for one degree of freedom. ~ The operator intertwines the energy quantizations, but it fails to be unitary. One could make ~ unitary by redefining the scalar product in 6tH, The geometric quantization of the harmonic oscillator in the energy representation was analyzed by Simms (197Sa). The argument that one should use the trivial metaplectic structure induced by the unique metaplectic structure on R2 is due to Blattner.