The Quantum Mechanics Solver 24 uniquely illustrates the application of quantum mechanical concepts to various fields of modern physics. It aims at encouraging the reader to apply quantum mechanics to research problems in fields such as molecular physics, condensed matter physics or laser physics. Advanced undergraduates and graduate students will find a rich and challenging source of material for further exploration. This book consists of a series of problems concerning present-day experimental or theoretical questions on quantum mechanics | Comments 235 with Y 4V0amd nh 2. We therefore obtain the desired relation I 1 - -1 xn n Yn 2 For n 4p 1 the perturbation increases the excitation energy and decreases An. For n 4p 3 it decreases the excitation energy and increases An. . For the ion n 11 one obtains the relation 1 11y 13 6000 6700 therefore y and AN 4330 A in good agreement with experiment. One also obtains AN3 6600 A which absorbs red light and gives a green color to the corresponding pigment. Note that the presence of the nitrogen atom yields A 3 A i whereas A03 A01. 13 11 13 11 . The distance between a node and an antinode of rfk x is dx nd 2k . For k n 1 2 and k n 3 2 which are the states of interest we will have respectively dx nd n 1 and dx nd n 3 . dx d if n is large. Consequently if a wave function has a node at the center it has an antinode in the vicinity of the two adjacent sites and vice versa. The argument is therefore similar to the answer to questions and with the reverse effect. The lines are red-shifted if n 4p 1 and they are blue-shifted if n 4p 3. Comments Many further details can be found in the article by John R. Platt The Chemical Bound and the Distribution of Electrons in Molecules D Conjugated Chains Handbuch Der Physik Volume XXXVII 2 p. 173 Springer-Verlag 1961 . This article is a very complete work on the applications of Quantum Mechanics in Chemistry. 23 Hyperfine Structure in Electron Spin Resonance Many molecular species such as free radicals possess an unpaired electron. The magnetic spin resonance of this electron called electron spin resonance ESR as opposed to nuclear magnetic resonance provides useful information about the electronic structure of the molecule as we shall see in this chapter. We assume here the following 1. Spin variables and space variables are independent both for electrons and for nuclei we are only interested in the former. 2. The spatial ground state of the unpaired electron is non-degenerate and one can .
