Let Ψ (x, t) = (A / (a2 + x2)) exp (-i 2 π E t / h ) be a normalized solution to Schrodinger’s equation for constants A, a, and E. (a) What is A in terms of a? (b) What is the potential function V(x)? (c) Evaluate Δx Δp. Is the uncertainty principle satisfied?

Let Ψ (x, t) = (A / (a2 + x2)) exp (-i 2 π E t / h ) be a normalized solution to Schrodinger’s equation for constants A, a, and E. (a) What is A in terms of a? (b) What is the potential function V(x)? (c) Evaluate Δx Δp. Is the uncertainty principle satisfied?

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Question

Let Ψ (x, t) = (A / (a2 + x2)) exp (-i 2 π E t / h ) be a normalized solution to Schrodinger’s equation
for constants A, a, and E.
(a) What is A in terms of a?
(b) What is the potential function V(x)?
(c) Evaluate Δx Δp. Is the uncertainty principle satisfied?

Expert Solution

Step 1: Determine the given data:

$straight psi left parenthesis straight x comma straight t right parenthesis equals fraction numerator straight A over denominator straight a squared plus straight x squared end fraction straight e to the power of negative fraction numerator straight i 2 straight pi Et over denominator straight h end fraction end exponent$ , this is a normalized wavefunction.

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