By W.-H Steeb

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**Example text**

For instance, if you walk in the street, your de Broglie 16 FROM KEPLER TO SCHRODINGER... AND BEYOND wavelength will have an order of magnitude of 10~ 35 m, which is undetectable by today's means. However, for an electron (m w 0, 9 x 1 0 - 3 0 kg) with velocity 106 m s _ 1 , we have A « 7 x 10~ 9 m, and this wavelength leads to observable diffraction patterns (it is comparable to the wavelength of certain X-rays). J. H. , Messiah, [101], Ch. 2, §6) showed that de Broglie was right. Davisson and Germer had set out to study the scattering of a collimated electron beam by a crystal of nickel.

I recommend the book [110] by A. ) Anyhow, there certainly are difficulties with that interpretation. As R. Omnes [109] notes, "... it is remarkable that so long after the discovery of quantum theory the most complete books devoted to the Copenhagen interpretation are all reprints of original articles or learned commentaries, becoming more and more commentaries upon commentaries as time goes on. In fact, these texts are devoted to an endless discussion of the difficulties of the "measurement problem" and of the difficulties facing interpretation, and philosophy of Science becomes more important than physics itself.

2 when \& is the wave function of a free particle. This result can be interpreted in the following way: the knowledge of the wave function provides us not only with a way of calculating "position statistics", but also tells us what the velocity of the particle associated with * should be a "long time" after a position measurement made at an arbitrary time t. 6 Quantum Mechanics in Phase Space As we said above, Heisenberg's inequalities (which mathematically only reflect the non-locality of the Fourier transform) have led many physicists to believe (and to vigorously advocate) that there can exist no such thing as "quantum mechanics in phase space".