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Dilute Bose gases have become accessible to experiments, furnishing us with simpler examples of superfluids. Among these are spin-aligned atomic hydrogen gas,t and liquid He 4 adsorbed in porous Vycor glass.:j: At sufficiently low temperatures, the interparticle potential may be summarized by only one parameter, the scattering length, which is a kind of effective hard-sphere diameter. The low-lying energy levels of a dilute Bose gas then correspond to those of a hard-sphere gas, which can be treated through the methods of pseudopotentials introduced in Section 10.5.

*An improved wave function that fits the data better is given by R. P. Feynman and M. Cohen, Phys. Rev. 102,1189 (1956). iT. J. Greytak and D. Kleppner, in New Trends in Atomic Physics, Vol. II (Les Houches 38) G. Greyberg and R. Stora, eds. (North-Holland, Amsterdam, 1984). tB. C. Crooker, B. Hebral, E. N. Smith, and J. D. Reppy, Phys. Rev. Lett. 51, 666 (1983). T. D. Lee, K. Huang, and C. N. Yang, Phys. Rev. 106,1135 (1957); see also K. Huang, op. cit.

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It should also be noted that the concept of time periods strictly depends on the frequency of the bars being shown in your chart If you are looking at a daily graph, then a period is a day So a 20-period moving average is a 20-day moving average If you are instead looking at the past ve days of trading activity on an hour-by-hour basis, each bar represents one hour of time, so the same moving average study would be a 20-hour moving average For the sake of simplicity, we will assume you are looking at a daily chart, so we will use terms such as 50-day moving average instead of the more precise and accurate 50-period moving average To edit a study, all you need to do is double-click the study that has been applied and appears on the right side of the technical studies editor.

l/J(r) =

!TT '

(13.88 1

and we have imposed periodic boundary conditions:

(13.891

when n is a vector whose components are independently 0, 1, 2, .... The appearance of the operator (ajar)r seems to complicate things, but actually the effect is quite simple. The operator has the property that

a; [rj(r)] r-O = j(O)

To wrap column text around a picture or other object, click the picture or object, click the Format tab, click the Wrap Text button and then click the type of wrapping that you want to apply.

(13.901

You can also click the study once and then click the Edit Study button When you do this, a Study Editor for that particular study will appear (Figure 65) and will contain the various controls germane to that study as well as the settings that are being used for it (which will typically be the default settings, unless you have changed them) Although every dialog box will be a little different, based on the study,.

The operator (ajar)r weeds out, so to speak, any singularity of the Ijr type in the function to which it is applied. * We treat the interaction as a perturbation on the ideal gas. The validity of the Hamiltonian is restricted by the conditions

ajv 1/ 3 1,

(13.91)

where v is the specific volume, and k is any wave number of an excited particle in the unperturbed state. For low-lying excited states, we assume (13.92 )

First we decompose the interaction into a part that has only diagonal matrix elements with respect to the unperturbed free-particle states and a part that has only off-diagonal elements. The part with diagonal matrix elements has been worked out and given in (A.36) of the Appendix, and discussed in Section 10.5. For the off-diagonal elements, we isolate a part that contains terms proportional to aoao or aiab. What is left contains terms both proportional to and independent of a o or ai. The matrix elements of the first part are of order N larger than those of the remaining part, which will be neglected. Thus we have

(13.93)

Now we replace both aoao and abai by N, and obtain an effective Hamiltonian:

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