By Pierre Bourdieu
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Of the realistic problem are turned oﬀ. The only possible conclusion is that the rotor constant B drastically changes the value of pcrit from the value predicted by the “anomaly” interpretation. We now proceed to demonstrate this assertion by studying analytically in a simple model how the critical value changes with nonzero B from the well known one for B = 0 (no rotation). In order to do so, we follow a didactic approach and take as our starting point the three dimensional Schr¨ odinger equation describing a particle of mass m in the potential V (r): V (r) = −α r2 −αb2 r4 (r < b) .
595. Obviously, there is no zero and hence no bound state. 75 -1 Fig. 2. β as a function of λ for b/a = 1000. 50 40 30 20 10 2000 Fig. 3. 595 and b/a = 1000. We conclude there exists a modiﬁcation in the critical coupling (from λ2 = 1/4) due to the change in the long range part of the interaction. 50 as b/a becomes very large, as expected. It is amusing that with the chosen value of b/a there is an increase of about 20 percent in the value of the critical coupling. The same feature occurs in models of molecular physics which have static dipole moments versus rotating physical dipole moments.
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