the Schrödinger equation for a finite well with width of and center at 0, the equation for the achieved quantum well can be written as:

::
::
::

Solution for above equations are well-known, only with different(modified) k and

::.

At the z = even-parity solution can be gained from
::.

By taking derivative of (5) and multiplying both sides by

::.

Dividing (6) by (5), even-parity solution function can be obtained,

::.