Consider the wave functionwhere A, λ, and ω are positive real constants. (We'll see in...

Consider the wave function

where A, λ, and ω are positive real constants. (We'll see in Chapter 2 what potential (V) actually produces such a wave function.)

(a) Normalize Ψ.

(b) Determine the expectation values of x and x2.

(c) Find the standard deviation of x. Sketch the graph of |Ψ|2, as a function of x, and mark the points (x + σ) and (x — σ), to illustrate the sense in which σ represents the “spread” in x. What is the probability that the particle would be found outside this range?