Solution to schrodinger equation near turning points:
Then .
So the schrodinger equation is:
define
Then .
Take asymptotic forms for Ai(y) and Bi(y) as y goes to and match
to get
,
. In general, use WKB connection formulas to get:
match the 2 classically allowed solutions.
. This means
Matching to dying exponential means Then
This is similar to the
Bohr-Sommerfeld quantization.