I selected this plausible measure for its mathematical simplicity, which allows for an explicit calculation of the theoretical expectation value and variance.
Assuming that the events are randomly distributed (with no two events at the same location), the expectation value of Pot in Equation A1 results from N(N - 1) /2 terms which--on average--contribute equally; that is, one can write
Table 1 displays the radial part R(Z, r) for the orbitals 1s to 6h of hydrogen-like atoms together with the corresponding radial expectation values (for Z = 1, wavefunctions taken from reference ).
In order to interpret the expectation values <r> as proton resonance lengths, following strictly the formalism of previous articles, it must be written:
Even though the experimenter had, through previous randomness tests, established the expectation value and variance for the scores, the use of the nonparametric Wilcoxon test was important because it permitted the independent observer a completely independent evaluation.
The score of each 128-bit unit has an expectation value of zero and a standard deviation of |Sigma~ = 94.
This is reflected in the formalism of standard quantum mechanics in the fact that the expectation value for an additive observable such as angular momentum has to be finite.
For instance, does it make any sense to say that an apparatus can have an infinite expectation value for an additive quantum mechanical observable?
12) So on the orthodox interpretation, the set of truths about a system's intrinsic state at a time is exhausted by listing its state-independent properties (mass, charge, spin-type), the eigenvalues of the observables of which it is in an eigenstate, and the expectation values for all observables of which it is not in an eigenstate.
All of the preceding rumination about chance was prompted by the question of what it could possibly mean to say that the expectation values (partly) characterize the intrinsic state of a system.
One other type of constraint which has received much attention, where Bayesian conditionalization and Jeffrey's rule are powerless, is represented by the case where the data are presented in the form of expectation values of observable random variables--sample averages, in fact.
Furthermore, not to use the rule of Bayesian conditionalization, but some other rule, like the principle of minimum information with a uniform prior and constraints in the form of expectation values, actually entails inconsistency, i.