Active Reading Solution: The Finite Square Well

Continuity at x=0: F=B
Continuity at x=L:
Differentiability requires that their first derivatives also match. Differentiating the solutions and then plugging in x=0 and x=L gives:
Differentiability at x=0:
Differentiability at x=L:

There is also a fifth condition. We have already demanded normalizability; to nail down the final constant, we need actual normalization.