Author: Tru Physics
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Problem 1.13 (Schroeder’s Intro to Thermal Physics)
Problem 1.13 A mole is approximately the number of protons in a gram of protons. The mass of a neutron is about the same as the mass of a proton, while the mass of an electron is usually negligible in comparison, so if you know the total number of protons and neutrons in a molecule…
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Problem 1.12 (Schroeder’s Intro to Thermal Physics)
Problem 1.12 Calculate the average volume per molecule for an ideal gas at room temperature and atmospheric pressure. Then take the cube root to get an estimate of the average distance between molecules. How does this distance compare to the size of a small molecule like or ? Solution: Problem 1.12
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Problem 1.11 (Schroeder’s Intro to Thermal Physics)
Problem 1.11 Rooms A and B are the same size, and are connected by an open door. Room A, however, is warmer (perhaps because its windows face the sun). Which room contains the greater mass of air? Explain carefully. Solution: Problem 1.11
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Problem 1.10 (Schroeder’s Intro to Thermal Physics)
Problem 1.10 Estimate the number of air molecules in an average-sized room. Solution: Problem 1.10
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Problem 1.9 (Schroeder’s Intro to Thermal Physics)
Problem 1.9 What is the volume of one mole of air, at room temperature and 1 atm pressure? Solution: Problem 1.9 Find more Schroeder solutions here.
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Problem 1.12 – Griffith’s Intro to QM
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…
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Problem 1.11 – Griffith’s Intro to QM
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…
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Problem 1.10 – Griffith’s Intro to QM
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…
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Problem 1.9 – Griffith’s Intro to QM
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…
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Problem 1.8 – Griffith’s Intro to QM
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…