Consider the wave function where A, , and are positive real constants. (Well see in Chapter

Consider the wave function

where A, λ, and ω are positive real constants. (We’ll see in Chapter 2 for what potential (V) this wave function satisfies the Schrödinger equation.)
(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?

Transcribed Image Text:

(x,1)= Aere-it