By H. Dekker

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**Extra resources for Classical and Quantum Mechanics of the Damped Harmonic Oscillator Dekker**

**Example text**

It is now generally accepted that all forces in nature result from the exchange of specific kinds of particles between the interacting entities. Between the time one of these entities emits such a "virtual" particle and the other absorbs it, there is a nonconservation of energy. Therefore, by the Heisenberg uncertainty principle, A; AE > h, there is only a finite amount of time during which the exchange can occur. Clearly, there is a relation between the mass of the exchanged particle and the possible range of the force: lighter (low E) virtual particles induce smaller violations of energy conservation and therefore can exist for longer periods of time, thus permitting longer-range forces.

For the degenerate case, it is of course (2 - 1)V = V. 414, which should now be approximately applicable to multistate mixing. 35. Finally, a third idealized case again concerns N degenerate levels, except that each level mixes with only the "adjacent" level (as shown in Fig. 11). N. —Kf which frequently occurs in heavy nuclei. Again, one level is lowered, but now the mixed levels are symmetrically distributed with respect to the initial energy and the lowest state is not lowered nearly as much.

Illustration of thenoncrossingof two admixed levels. An example is useful. Suppose R = 10. 0099. In fact, even for R = 4, Eqs. 12 are already quite satisfactory: /? is correct to belter than 10 percent and AEs to 6 percent. Except in the case of rather strong mixing, Eqs. 12 thus provide quite accurate (instantaneous) results for iwo-slate mixing. There is one other important aspect of two-state mixing. Suppose we consider two states, 1 and 2, whose energies depend on some nuclear structure parameter x (as illustrated schematically in Fig.