Problem 1.3 | Griffiths' Introduction to Quantum Mechanics | 3rd Edition

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Problem 1.3
Consider the gaussian distribution ρ(x) = Ae^(−λ(x−a)^2)), where A, a, and λ are positive real constants. (The necessary integrals are inside the back cover.)
(a) Use Equation 1.16 to determine A.
(b) Find {x}, {x^2}, and σ.
(c) Sketch the graph of ρ(x).

In this video, we solve Problem 1.3 in Griffiths' Introduction to Quantum Mechanics (3rd Edition) as part of a series of solutions to the textbook's questions.
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Комментарии
Автор

Aren't we supposed to take the integral of the ρ^2 instead of the ρ in order to find the A by normalizing the function?

ananasbozukdaily
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This is most excellent, thank you! for part a (find A) your closed form solution was really helpful, I would never have figured it out. For part b, maybe 7 lines of code in Mathematica got me there, not all that tiresome integration by parts, variable substitution etc. Call me lazy :) Thanks again!

photon
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hi! Where you find the integration table?

marianesilva