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Are quanta real: A Galilean dialogue by J.M. Jauch

By J.M. Jauch

"... thought-provoking and pleasant. i think that anybody attracted to nature's private secrets and techniques might locate nice stimulation during this charmingly written little gem of a book." -- Douglas Hofstadter"... strange, pleasant, nonmathematical book... The reader is left in amusement and admiration." -- clinical American"This is an excellent book... " -- American magazine of Physics"... this resourceful work... elucidates the distinction among the classical, deterministic notions that appear inbred and the unusual habit of the microscopic quantum world.... by way of resurrecting Galileo's 3 questing neighbors, Jauch is ready to pose questions a pupil wish to ask yet too usually is inhibited from doing so." -- the most important ReporterAn authority on either quantum mechanics and the paintings of Galileo, J. M. Jauch wrote this fascinating discourse in imitation of Galileo's celebrated discussion "Two significant structures of the World." The discussion shape is a laugh in addition to profitable and appeals to the scholar of quantum mechanics, the thinker or historian of technological know-how, and the lay individual.

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Nun berechnen wir die totalen Str¨ ome in den Gebieten A und C: A: ψ(x) = ψein (x) + ψR (x) = e+ik0 x + α− e−ik0 x j = = C: ¯h (ψ ∗ ψ − ψψ ∗ ) 2mi ¯h ∗ ∗ ∗ + ψR ψR − ψR ψR ) = jein + jR (ψ ∗ ψ − ψein ψein 2mi ein ein j = jT , wobei sich die gemischten Terme in A fortheben. Aus der Konstanz des Stromes folgt nun jein + jR = jT und daher 1= jR jT jR jT − = + = T +R, jein jein jein jein 50 3 Wellenmechanik in einer Dimension was zu zeigen war. Der Transmissionskoeffizient f¨ ur den Potenzialtopf lautet explizit T = 1+ ε2− sin2 kL 4 −1 , wobei ε2− = V02 .

2 Endlicher Potenzialtopf E/ε 3 6 9 11 12 14 39 n (1, 1, 1) (2, 1, 1), (1, 2, 1), (1, 1, 2) (2, 2, 1), (2, 1, 2), (1, 2, 2) (3, 1, 1), (1, 3, 1), (1, 1, 3) (2, 2, 2) (3, 2, 1), . . A. mehrere Eigenzust¨ ande zum gleichen Eigenwert. B. Verwendung in vereinfachten Modellen f¨ ur das Deuteron oder die Bewegung von Elektronen bei Anwesenheit von St¨orstellen. Das zu l¨osende Problem lautet − 1. ¯ 2 ∂ 2 ψ(x) h + V (x)ψ(x) = E ψ(x) 2m ∂x2 ∞ |ψ(x)|2 dx = 1 2. −∞ ψ stetig , ψ stetig. 3. 1 Gebundene Zust¨ ande Sei E < 0.

Das wiederholt man und variiert den Parameter E dabei so lange, bis ψ(L) = 0 erf¨ ullt ist. F¨ ur dieses einfache System gibt es aber auch eine analytische L¨ osung. Mit . 2mE >0 k2 = h2 ¯ haben wir ψ (x) = −k2 ψ(x) f¨ ur 0 ≤ x ≤ L , ψ(0) = ψ(L) = 0 . Die L¨osung ist klar: ψ(x) = A sin kx + B cos kx . Aus ψ(0) = 0 folgt B = 0 und somit ψ(x) = A sin kx. Die zweite Randbedingung ψ(L) = 0 erfordert sin kL = 0. Dies ist erf¨ ullt, falls kL = nπ , n ∈ Z. Die negativen n entfallen, da die zugeh¨ origen L¨ osungen proportional zu denen mit positivem n sind.

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