Use the following wave function $\Psi(x, t)$ to find the following information $\Psi(x, t) = \left(\frac{2am}{\pi h}\right)^{1/4} e^{-amx^2/h}e^{-ait}$ (4) Find $\Delta x = \sqrt{\langle x^2 \rangle - \langle x \rangle^2}$ (5) What would $\Delta p$ to be in order for $\Delta x$ to agree with the uncertainty principle? Important integral: $2 \int_0^\infty x^2 e^{-ax^2} dx = \frac{1}{2a} \sqrt{\frac{\pi}{a}}$

          Use the following wave function $\Psi(x, t)$ to find the following information
$\Psi(x, t) = \left(\frac{2am}{\pi h}\right)^{1/4} e^{-amx^2/h}e^{-ait}$
(4) Find $\Delta x = \sqrt{\langle x^2 \rangle - \langle x \rangle^2}$
(5) What would $\Delta p$ to be in order for $\Delta x$ to agree with the uncertainty principle?
Important integral: $2 \int_0^\infty x^2 e^{-ax^2} dx = \frac{1}{2a} \sqrt{\frac{\pi}{a}}$

Use the following wave function Ψ(x, t) to find the following information
Ψ(x, t) = ((2am)/(π h))^1/4 e^-amx^2/he^-ait
(4) Find Δ x = √(⟨ x^2 ⟩ - ⟨ x ⟩^2)
(5) What would Δ p to be in order for Δ x to agree with the uncertainty principle?
Important integral: 2 ∫0^∞ x^2 e^-ax^2 dx = (1)/(2a)√((π)/(a))

Added by Irene M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Yatu Khandelwal

Step 1

The given wave function is (x,t) = 2am 1/4 e^(-amx)/(he^(-ait)nh). Show more…

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Use the following wave function (x,t) to find the following information: 2am 1/4 (x,t) = e^(-amx)/(he^(-ait)nh) Find x = x^2 - (x)^2 What would p need to be in order for x to agree with the uncertainty principle? Important integral: 2 âˆ« x^2e^(-ax^2) dx = 1/7