Consider the 1D time-independent Schrodinger equation ħ² ď² 2m dg² + V (2)) v. with the potential where to is a parameter. (a) Show that (- V(x) = ħ² mx² = Ev sech² (2.), 1 = A sech (2) is a solution of the Schrodinger equation. (b) Determine the energy E₁ of the eigenfunction ₁. (c) Sketch V(x), ₁(x), and E₁ in the usual manner, and find the locations of the classical turning points.
Consider the 1D time-independent Schrodinger equation ħ² ď² 2m dg² + V (2)) v. with the potential where to is a parameter. (a) Show that (- V(x) = ħ² mx² = Ev sech² (2.), 1 = A sech (2) is a solution of the Schrodinger equation. (b) Determine the energy E₁ of the eigenfunction ₁. (c) Sketch V(x), ₁(x), and E₁ in the usual manner, and find the locations of the classical turning points.
Related questions
Question
Transcribed Image Text: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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 6 images
