In this paper, we have considered the generalized bi-axially symmetric Schr?dinger equation ?~2φ/?x~2+?~2φ/?y~2+(2ν/x)?φ/?x+(2μ/y)?φ/?y+ {K~2- V(r)}φ = 0
We recall some properties of the Segal-Bargmann transform; and we establish for this transform qualitative uncertainty principles: local uncertainty principle,