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Consider the 1D time-independent Schrodinger equation
ħ² d²
₁
y Ev
2m dz² + V (2)) =
with the potential
where to is a parameter.
(a) Show that
V(x) =
ħ²
mx²
sech² (2)
h (2)
₁ = A sech
is a solution of the Schrodinger equation.
(b) Determine the energy E₁ of the eigenfunction V₁.
(c) Sketch V(x), 4₁(x), and E₁ in the usual manner, and find the locations of the classical
turning points.

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