Author: Tru Physics
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Problem 1.7 – Griffith’s Intro to QM
Problem 1.7 Calculate . Answer: . This is an instance of Ehrenfest’s theorem, which asserts that expectation values obey the classical laws. Solution: Problem 1.7
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Problem 1.6 – Griffith’s Intro to QM
Problem 1.6 Why can’t you do integration-by-parts directly on the middle expression in Equation 1.29—pull the time derivative over onto , note that , and conclude that ? Solution: Problem 1.6
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Problem 1.5 – Griffith’s Intro to QM
Problem 1.5 Consider the wave function where , , and are positive real constants. (We’ll see in Chapter 2 for what potential (V) this wave function satisfies the Schrödinger equation.) (a) Normalize .(b) Determine the expectation values of and .(c) Find the standard deviation of . Sketch the graph of , as a function of…
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Problem 1.4 – Griffith’s Intro to QM
Problem 1.4 At time a particle is represented by the wave function where , , and are (positive) constants.(a) Normalize (that is, find , in terms of and ).(b) Sketch , as a function of .(c) Where is the particle most likely to be found, at ?(d) What is the probability of finding the particle…
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Problem 1.3 – Griffith’s Intro to QM
Problem 1.3 Consider the gaussian distribution where , , and are positive real constants. (The necessary integrals are inside the back cover.)(a) Use Equation 1.16 to determine .(b) Find , , and .(c) Sketch the graph of . Solution: Problem 1.3
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Problem 1.2 – Griffith’s Intro to QM
Problem 1.2 (a) Find the standard deviation of the distribution in Example 1.2. (b) What is the probability that a photograph, selected at random, would show a distance x more than one standard deviation away from the average? Solution: Problem 1.2 Solution
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Problem 1.1 – Griffith’s Intro to QM
Problem 1.1: For the distribution of ages in the example in Section 1.3.1:(a) Compute and .(b) Determine for each , and use Equation 1.11 to compute the standarddeviation.(c) Use your results in (a) and (b) to check Equation 1.12. Solution:Problem 1.1 Solution Find more Griffith’s solutions here.