Tag: Griffith&#8217;s Introduction to Quantum Mechanics 3rd Edition

Problem 1.15 Show that for any two (normalizable) solutions to the Schrödinger equation (with the same ), and . Solution:

Problem 1.12 – Griffith’s Intro to QM

—

by

Problem 1.12 What if we were interested in the distribution of momenta , for the classical harmonic oscillator (Problem 1.11(b)). (a) Find the classical probability distribution (note that ranges from to ).(b) Calculate , , and .(c) What’s the classical uncertainty product, , for this system? Notice that this product can be as small as…

Problem 1.11 – Griffith’s Intro to QM

—

by

Problem 1.11 [This problem generalizes Example 1.2.] Imagine a particle of mass and energy in a potential well , sliding frictionlessly back and forth between the classical turning points ( and in Figure 1.10). Classically, the probability of finding the particle in the range (if, for example, you took a snapshot at a random time…

Problem 1.10 – Griffith’s Intro to QM

—

by

Problem 1.10 Consider the first 25 digits in the decimal expansion of (3, 1, 4, 1, 5, 9, … ). (a) If you selected one number at random, from this set, what are the probabilities of getting each of the 10 digits?(b) What is the most probable digit? What is the median digit? What is…

Problem 1.9 – Griffith’s Intro to QM

—

by

Problem 1.9 A particle of mass m has the wave function , where and are positive real constants. (a) Find .(b) For what potential energy function, , is this a solution to the Schrödinger equation?(c) Calculate the expectation values of , , , and .(d) Find and . Is their product consistent with the uncertainty…

Problem 1.8 – Griffith’s Intro to QM

—

by

Problem 1.8 Suppose you add a constant to the potential energy (by “constant” I mean independent of as well as ). In classical mechanics this doesn’t change anything, but what about quantum mechanics? Show that the wave function picks up a time-dependent phase factor: . What effect does this have on the expectation value of…

Problem 1.7 – Griffith’s Intro to QM

—

by

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

Problem 1.6 – Griffith’s Intro to QM

—

by

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

Problem 1.5 – Griffith’s Intro to QM

—

by