Physlet Quantum Physics by Belloni, Christian, and Cox: Problem 6.5

6.1: Probability Distributions and Statistics
6.2: Classical Probability Distributions for Moving Particles
6.3: Exploring Classical Probability Distributions
6.4: Probability and Wave Functions
6.5: Exploring Wave Functions and Probability
6.6: Exploring Wave Functions and Expectation Values

Problem 6.5: Calculate expectation values of x for an arbitrary state

Please wait for the animation to completely load.

The wave function shown in the upper left-hand graph, is for a particle in an infinite square well of length L = 2. You may import a function of x and calculate the integral of that function times the probability density. In the animation, ħ = 2m = 1.

Check that the state is normalized. What f(x) must you use to do this?
What is the expectation value of x?
What is the expectation value of x²?
What is Δx?

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