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0. Math Review
Math Review: Study with Video Lessons, Practice Problems & Examples
Back to all problems
29PRACTICE PROBLEM
A quantum particle moves freely in the positive x-direction following the equation ψ(x,t) = A[ei(k1x - ω1t) + ei(k2x - ω2t)]. Suppose k2 = 4k1 = 4k and a maximum of the probability distribution function |ψ(x,t)|2 occurs at t = 0 and x = 0. i) Given that ω = ħk2/2m, determine the least positive value of x that gives a maximum in the probability distribution function at t = 4π/ω. ii) Use the result in part i) to determine the average speed in the negative x-direction of the probability distribution function. Also, determine the average speed using vav = (ω2 - ω1)/(k2 - k1).
A quantum particle moves freely in the positive x-direction following the equation ψ(x,t) = A[ei(k1x - ω1t) + ei(k2x - ω2t)]. Suppose k2 = 4k1 = 4k and a maximum of the probability distribution function |ψ(x,t)|2 occurs at t = 0 and x = 0. i) Given that ω = ħk2/2m, determine the least positive value of x that gives a maximum in the probability distribution function at t = 4π/ω. ii) Use the result in part i) to determine the average speed in the negative x-direction of the probability distribution function. Also, determine the average speed using vav = (ω2 - ω1)/(k2 - k1).