The Quantum Mechanics Solver 12 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 | 108 11 The EPR Problem and Bell s Inequality which violates unquestionably Bell s inequality and is consistent with the quantum mechanical prediction. It is therefore not possible to find a local hidden variable theory which gives a good account of experiment. Fig. . Variation of g 0 as defined in the text Section References A. Einstein B. Podolsky and N. Rosen Phys. Rev. 47 777 1935 . . Bell Physics 1 195 1964 see also J. Bell Speakable and unspeakable in quantum mechanics Cambridge University Press Cambridge 1993 . The experimental data shown here are taken from A. Aspect P. Grangier and G. Roger Phys. Rev. Lett. 49 91 1982 A. Aspect J. Dalibard and G. Roger Phys. Rev. Lett. 49 1804 1982 . 12 Schrodinger s Cat The superposition principle states that if a and are two possible states of a quantum system the quantum superposition o b yf2 is also an allowed state for this system. This principle is essential in explaining interference phenomena. However when it is applied to large objects it leads to paradoxical situations where a system can be in a superposition of states which is classically self-contradictory antinomic . The most famous example is Schrodinger s cat paradox where the cat is in a superposition of the dead and alive states. The purpose of this chapter is to show that such superpositions of macroscopic states are not detectable in practice. They are extremely fragile and a very weak coupling to the environment suffices to destroy the quantum superposition of the two states o and b . The Quasi-Classical States of a Harmonic Oscillator In this chapter we shall consider high energy excitations of a one-dimensional harmonic oscillator of mass m and frequency w. The Hamiltonian is written .2 -I H ----1 mx2 X2 . 2m 2 We denote the eigenstates of H by n . The energy of the state n is En n 1 2 hw. . Preliminaries. We introduce the operators X p y mhw and the annihilation and creation operators a TT A xymx h P 1 x ip 2 V . N â â
