<< Miscellaneous`PhysicalConstants`

g = AccelerationDueToGravity;
ℏ =  PlanckConstantReduced;
m =  1 kg;
Joule  =  ((kg (Meter^2))/(Second^2));

(Subscript[x, 0]) = Expand[(((((ℏ^2)/(2  (m^2) g))))^(1/3))]

(Subscript[t, 0]) = (ℏ/(m g (Subscript[x, 0])))

(Subscript[E, 0])  =  m g (Subscript[x, 0])

DSolve[y''[x]==x y[x],y,x]

AiryBi increases unboundedly for x-> ∞

Plot[AiryAi[x], {x, -10, 10}, PlotRange -> All];

rt = 
      FindRoot[AiryAi[x] == 0, {x, -2}]
rt = 
      FindRoot[AiryAi[x] == 0, {x, -4}]
rt = 
      FindRoot[AiryAi[x] == 0, {x, -6}]
rt = 
      FindRoot[AiryAi[x] == 0, {x, -7}]
rt = FindRoot[AiryAi[x] == 0, {x, -8}]