Consider the double delta function potential where and a are positive constants (a) Sketch this potential (b) How many bound states does it possess Find the allowed energies, for 2 m and for 2 4m, and sketch the wave functions (c) What are the bound state energies in the limiting cases (i) 0 and (ii) (holding fixed) Explain why your answers are reasonable, by comparison with the single delta function well V(x) a 8(x a) 8(x a) ,

Question: Consider the double delta-function potential where and a are positive constants. (a) Sketch this potential. (b) How many bound states does it possess? Find

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.

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

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