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The Quantum Mechanics Solver 7

The Quantum Mechanics Solver 7 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 | 4.2 Solutions 53 a broader central peak and lateral fringes of decreasing amplitude. However the position of the central peak does not depend on the velocity and it is therefore not shifted if the neutron beam has some velocity dispersion. On the contrary in the method of question 4.1.5 the position of the central peak depends directly on the velocity. A dispersion in v will lead to a corresponding dispersion of the position of the peak we want to measure. The first method is highly preferable. 4.1.7. Numerically for An 31 A v h MnXn 128 m s. Experimentally one obtains an accuracy 8w0 w0 Jyn yn 4.6 x 10 7. For B 1 T the angular frequency is w0 yn Bo 1.8 x 108 s-1 which gives 8w0 2n 13 Hz and b 2.4 m. Actually one can improve the accuracy considerably by analysing the shape of the peak. In the experiment reported in the reference quoted below the length b is 2 m and the field is Bo 0.05 T i.e. an angular frequency 20 times smaller than above . Reference G.L. Greene N.F. Ramsey W. Mampe J.M. Pendlebury K.F. Smith W.D. Dress P.D. Miller and P. Perrin Phys. Rev. D 20 2139 1979 . 5 Analysis of a Stern-Gerlach Experiment We analyze a Stern-Gerlach experiment both experimentally and from the theoretical point of view. In the experimental setup considered here a monochromatic beam of neutrons crosses a region of strongly inhomogeneous magnetic field and one observes the outgoing beam. 5.1 Preparation of the Neutron Beam Neutrons produced in a reactor are first cooled i.e. slowed down by crossing liquid hydrogen at 20 K. They are incident on a monocrystal for instance graphite from which they are diffracted. To each outgoing direction there corresponds a well-defined wavelength and therefore a well-defined momentum. A beryllium crystal acts as a filter to eliminate harmonics and the vertical extension of the beam is controlled by two gadolinium blocks which are opaque to neutrons separated by a thin sheet of transparent aluminum of thickness a which constitutes the .