ON THE PROBABILITY INTERPRETATION OF THE BOUND STATE WAVE FUNCTION OF THE MESON

Abstract：

The probability interpretation of the bound state meson wave functions is discussed by taking the O- meson wave function solved for the nearly flat bottom potential asan example. On the one hand, given a probability amplitude sense to the three dimen-sional wave function of the meson in the configuration space obtained under the equaltime limit of the four dimensional covariant wave functional solved from the B-S equal-tion, the averaged radius<r ²> of the meson can be calculated. On the other hand, theelectromagnetic average radius <r²> is evaluated from the slope at the origin of thespace-like electromagnetic form factor of the meson calculated directly from the fourdimensional B-S wave function. The two averaged values are compared and turn outto be in good coincidence (except for the case of scalar coupling, in which the differenceis about 30%). This shows that though the four dimensional B-S wave function doesnot possess a definite sense of probability amplitude, nevertheless, it might be plausibleto give such a sense to the three dimensional configuration space wave function of themeson obtained from the four dimensional one under the equal time limit.