*Problem 1.5 Consider the wave function ¥(x. t) = Ae¬lx1e-iwr, where A, 2, and w are positive real constants. (We’ll see in Chapter 2 what potential (V) actually produces such a wave function.) (a) Normalize ¥. (b) Determine the expectation values of x and x2. 12A good mathematician can supply you with pathological counterexamples, but they do not arise in physics: for us the vave function always goes to zero infinity at
*Problem 1.5 Consider the wave function ¥(x. t) = Ae¬lx1e-iwr, where A, 2, and w are positive real constants. (We’ll see in Chapter 2 what potential (V) actually produces such a wave function.) (a) Normalize ¥. (b) Determine the expectation values of x and x2. 12A good mathematician can supply you with pathological counterexamples, but they do not arise in physics: for us the vave function always goes to zero infinity at
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*Problem 1.5 Consider the wave function
¥ (x, t) = Ae-Alxle-iwt
where A, 2, and w are positive real constants. (We'il see in Chapter 2 what potential
(V) actually produces such a wave function.)
(a) Normalize Y.
(b) Determine the expectation values of x and x2.
12A good mathematician can supply you with pathological counterexamples, but they do not arise
in physics; for us the wave function always goes to zero at infinity.
Section 1.5: Momentum
15
(c) Find the standard deviation of x. Sketch the graph of |4|², as a function
of x, and mark the points ((x)+o) and ((x) – o), to illustrate the sense in
which o represents the "spread" in x. What is the probability that the particle
would be found outside this range?
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