WKB近似
Ai  ( + y ) ∼ 1 2 e − 2 3 y 3 2 π y 1 4 , {\displaystyle \operatorname {Ai} (+y)\sim {\frac {1}{2}}{\dfrac {e^{-{\frac {2}{3}}y^{\frac {3}{2}}}}{{\sqrt {\pi }}\,y^{\frac {1}{4}}}},} Ai  ( − y ) ∼ sin  ( 2 3 y 3 2 + π 4 ) π y 1 4 {\displaystyle \operatorname {Ai} (-y)\sim {\frac {\sin \left({\frac {2}{3}}y^{\frac {3}{2}}+{\frac {\pi }{4}}\right)}{{\sqrt {\pi }}\,y^{\frac {1}{4}}}}}
Bi  ( y ) ∼ e 2 3 y 3 2 π y 1 4 , {\displaystyle \operatorname {Bi} (y)\sim {\frac {e^{{\frac {2}{3}}y^{\frac {3}{2}}}}{{\sqrt {\pi }}\,y^{\frac {1}{4}}}},} Bi  ( − y ) ∼ cos  ( 2 3 y 3 2 + π 4 ) π y 1 4 {\displaystyle \operatorname {Bi} (-y)\sim {\frac {\cos \left({\frac {2}{3}}y^{\frac {3}{2}}+{\frac {\pi }{4}}\right)}{{\sqrt {\pi }}\,y^{\frac {1}{4}}}}}
E = V ( a ) {\displaystyle E=V(a)} である点を挟んでWKB近似解を接続するには、