The Quantum Mechanics Solver 13 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 | 118 12 Schrodinger s Cat . The statistical mixture of Bob leads to the same momentum distribution as that measured by Alice the N 2 oscillators in the state a all lead to a mean momentum p0 and the N 2 oscillators in the state a to p0. Up to this point there is therefore no difference and no paradoxical behavior related to the quantum superposition . . In the X variable the resolution of the detector satisfies SX 1 a P Alice therefore has a sufficient resolution to observe the oscillations of the function cos2 X 2 n 4 in the distribution P X . The shape of the distribution will therefore reproduce the probability law of X drawn on figure . a modulation of period hn2 2ma 2œ 1 2 with a Gaussian envelope. . If Bob performs a position measurement on the N 2 systems in the state a he will find a Gaussian distribution corresponding to the probability law P X k -0a X 2 k exp X 2. He will find the same distribution for the N 2 systems in the state a . The sum of his results will be a Gaussian distribution which is quite different from the result expected by Alice. The position measurement should in principle allow one to discriminate between the quantum superposition and the statistical mixture. . The necessary resolution is Sx C jil mA 5 10 26 m. Unfortunately it is impossible to attain such a resolution in practice. Section The Fragility of a Quantum Superposition . We have E t hW ao 2e -Yt 1 2 this energy decreases with time. After a time much longer than y - 1 the oscillator is in its ground state. This dissipation model corresponds to a zero temperature environment. The mean energy acquired by the environment E 0 E t is for 2yt C 1 AE t 2hw ao 2 yt. . a The probability distribution of the position keeps its Gaussian envelope but the contrast of the oscillations is reduced by a factor r . b The probability distribution of the momentum is given by P p A 1 p 2 h-ai p 2 2n Re iP -ai p ai p Since the overlap of the two
