By Sakurai J.J.

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**Extra resources for Modern Quantum Mechanics and solutions for the exercices**

**Example text**

The precise way in which the discrete nature of ionization determines fundamental limits of accuracy depends on the measurement method in question and will be dealt with in Chap. 7. In preparation, we discuss here the following question: Given a certain track length L – for example, the part of the track collected onto one wire – with what precision is the centre of gravity of the discretely deposited ionization located along the track? If the coordinate along the track is x, and in the ith cluster we have ni electrons, then the centre of gravity is at m x¯ = ∑ (xi ni ) i=1 m ∑ ni .

49). The distributions of Fig. 3 in this range of m . Relative widths W /Imp of measured pulse-height distributions quoted by Walenta [WAL 81] are shown in Fig. 11 as a function of the gas sample thickness pL. The ratio decreases with increasing pL. 37) Imp 1 Imp 2 then from Fig. 4. Since the ionization distribution depends only on the cluster-size distribution and the number of clusters, it depends on the sample length L and the gas pressure p through the product pL. Fig. 12 Measured relative widths of pulse-height distributions as collected by Walenta [WAL 81].

83) 1/ ∑ k, the exponential may be expanded to 1 P2 (T ) → k1 k4 P0 T 2 . e. T 1/ ∑ k, the exponential vanishes, so that P2 (T ) → k1 k4 P0 T. 79). 85) unless k1 or k2 dominates ∑ k. In our approximation that treats P0 as an infinite reservoir, we assume that k1 ∑ k; then a similar condition holds for k2 (except for special circumstances in which σ12 is orders of magnitude larger than σ10 ): 1 σ01 σ12 P0 φ 2 T 2 (small T, small φ ), 2 σ01 σ12 P2 (T ) → P0 φ 2 T (large T, small φ ). 87) (b) General Case.

### Modern Quantum Mechanics and solutions for the exercices by Sakurai J.J.

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