Consider the double delta-function potential where and a are positive constants. (a) Sketch this potential. (b)

Consider the double delta-function potential

where α and a are positive constants.
(a) Sketch this potential.
(b) How many bound states does it possess? Find the allowed energies, for α = ћ² /mα and for α = ћ² /4mα, and sketch the wave functions.
(c) What are the bound state energies in the limiting cases (i) α → 0 and (ii) α → ∞ (holding α fixed)? Explain why your answers are reasonable, by comparison with the single delta-function well.

Transcribed Image Text:

V(x) = -a [8(x + a) + 8(x-a)],