This is a strictly qualitative problemno calculations allowed Consider the double square well potential (Figure 2 20) Suppose the depth V 0 and the width are fixed, and large enough so that several bound states occur (a) Sketch the ground state wave function 1 and the first excited state 2 , (i) fo...

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This is a strictly qualitative problemno calculations allowed! Consider the double square well potential (Figure 2.20). Suppose

Question:

This is a strictly qualitative problem—no calculations allowed! Consider the “double square well” potential (Figure 2.20). Suppose the depth V₀ and the width α are fixed, and large enough so that several bound states occur.
(a) Sketch the ground state wave function Ψ₁ and the first excited state Ψ₂, (i) for the case b = 0, (ii) for b ≈ α, and (iii) for b >> α.
(b) Qualitatively, how do the corresponding energies (E₁ and E₂) vary, as b goes from 0 to ∞? Sketch E₁ (b) and E₂ (b) on the same graph.
(c) The double well is a very primitive one-dimensional model for the potential experienced by an electron in a diatomic molecule (the two wells represent the attractive force of the nuclei). If the nuclei are free to move, they will adopt the configuration of minimum energy. In view of your conclusions in (b), does the electron tend to draw the nuclei together, or push them apart? (Of course, there is also the internuclear repulsion to consider, but that’s a separate problem.)

Figure 2.20