Tag: Solutions

Problem 10.1 Rutherford scattering. An incident particle of charge and kinetic energy scatters off a heavy stationary particle of charge (a) Derive the formula relating the impact parameter to the scattering angle. Answer: (b) Determine the differential scattering cross-section. Answer: (c) Show that the total cross-section for Rutherford scattering is infinite. Solution: Problem 10.1 Solution…

Problem 2.22 – Griffith’s Intro to QM

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Problem 2.22 Evaluate the following integrals: (a) (b) (c) Solution: Problem 2.22 Solution (Download)

Problem 2.18 – Griffith’s Intro to QM

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Problem 2.18 Find the probability current, (Problem 1.14) for the free particle wave function Equation 2.95. Which direction does the probability flow? Solution: Problem 2.18 Solution (Download)

Problem 2.17 – Griffith’s Intro to QM

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Problem 2.17 Show that and are equivalent ways of writing the same function of and determine the constants and in terms of and and vice versa. Comment: In quantum mechanics, when the exponentials represent traveling waves, and are most convenient in discussing the free particle, whereas sines and cosines correspond to standing waves, which arise…

Problem 2.15 – Griffith’s Intro to QM

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Problem 2.15 Use the recursion formula (Equation 2.85) to work out and Invoke the convention that the coefficient of the highest power of is to fix the overall constant. Solution: Problem 2.15 Solution (Download)

Problem 1.13 – Griffith’s Intro to QM

May 24, 2023

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Problem 1.13 Check your results in Problem 1.11(b) with the following “numerical experiment.” The position of the oscillator at time t is You might as well take (that sets the scale for time) and (that sets the scale for length). Make a plot of at 10,000 random times, and compare it with Hint: In Mathematica,…

Problem 9.3 – Griffith’s Intro to QM

May 23, 2023

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Problem 9.3 Use Equation 9.23 to calculate the approximate transmission probability for a particle of energy that encounters a finite square barrier of height and width Compare your answer with the exact result (Problem 2.33), to which it should reduce in the WKB regime Solution: Problem 9.3 Solution (Download)

Problem 8.1 – Griffith’s Intro to QM

May 22, 2023

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Problem 8.1 Use a gaussian trial function (Equation 8.2) to obtain the lowest upper bound you can on the ground state energy of (a) the linear potential: ; (b) the quartic potential: V(x)=\alpha x^4.$ Solution: Problem 8.1 Solution (Download)

Problem 7.3 – Griffith’s Intro to QM

May 11, 2023

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