Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 2.4, Problem 2.18P
To determine
The probability current and direction of probability flow.
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Problem 2.29 Analyze the odd bound state wave functions for the finite square
well. Derive the transcendental equation for the allowed energies, and solve it
graphically. Examine the two limiting cases. Is there always an odd bound state?
Problem 2.11
(a) Compute (x). (p). (x²), and (p²), for the states yo (Equation 2.60) and 1 (Equation
2.63), by explicit integration. Comment: In this and other problems involving the
harmonic oscillator it simplifies matters if you introduce the variable = √mo/hx
and the constanta (m/h)¹/4
(b) Check the uncertainty principle for these states.
(c) Compute (T) and (V) for these states. (No new integration allowed!) Is their sum
what you would expect?
Figure 1.30
Chapter 2 Solutions
Introduction To Quantum Mechanics
Ch. 2.1 - Prob. 2.1PCh. 2.1 - Prob. 2.2PCh. 2.2 - Prob. 2.3PCh. 2.2 - Prob. 2.4PCh. 2.2 - Prob. 2.5PCh. 2.2 - Prob. 2.6PCh. 2.2 - Prob. 2.7PCh. 2.2 - Prob. 2.8PCh. 2.2 - Prob. 2.9PCh. 2.3 - Prob. 2.10P
Ch. 2.3 - Prob. 2.11PCh. 2.3 - Prob. 2.12PCh. 2.3 - Prob. 2.13PCh. 2.3 - Prob. 2.14PCh. 2.3 - Prob. 2.15PCh. 2.3 - Prob. 2.16PCh. 2.4 - Prob. 2.17PCh. 2.4 - Prob. 2.18PCh. 2.4 - Prob. 2.19PCh. 2.4 - Prob. 2.20PCh. 2.4 - Prob. 2.21PCh. 2.5 - Prob. 2.22PCh. 2.5 - Prob. 2.23PCh. 2.5 - Prob. 2.24PCh. 2.5 - Prob. 2.25PCh. 2.5 - Prob. 2.26PCh. 2.5 - Prob. 2.27PCh. 2.5 - Prob. 2.28PCh. 2.6 - Prob. 2.29PCh. 2.6 - Prob. 2.30PCh. 2.6 - Prob. 2.31PCh. 2.6 - Prob. 2.32PCh. 2.6 - Prob. 2.34PCh. 2.6 - Prob. 2.35PCh. 2 - Prob. 2.36PCh. 2 - Prob. 2.37PCh. 2 - Prob. 2.38PCh. 2 - Prob. 2.39PCh. 2 - Prob. 2.40PCh. 2 - Prob. 2.41PCh. 2 - Prob. 2.42PCh. 2 - Prob. 2.44PCh. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - Prob. 2.47PCh. 2 - Prob. 2.49PCh. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 2 - Prob. 2.52PCh. 2 - Prob. 2.53PCh. 2 - Prob. 2.54PCh. 2 - Prob. 2.58PCh. 2 - Prob. 2.63PCh. 2 - Prob. 2.64P
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- Show that a gaussian psi (x) = e ^(-ax^2) can be an eigenfunction of H(hat) for harmonic oscillator 1. Compute T(hat)*psi 2. Compute Vhat* psi - assume V operator is 1/2w^2x^2 3. Write out Hbar*psi and identify terms so Hber*psi=E*psi is true 4. From cancellation find a 5. insert back a to Schrodinger eq above and find Earrow_forwardProblem 2.15 In the ground state of the harmonic oscillator, what is the probability (correct to three significant digits) of finding the particle outside the classically allowed region? Hint: Classically, the energy of an oscillator is E = (1/2)ka² = (1/2)mw²a², where a is the amplitude. So the "classically allowed region" for an oscillator of energy E extends from -√2E/mw² to +√2E/mw². Look in a math table under "Normal Distribution" or "Error Function" for the numerical value of the integral.arrow_forwardProblem 3.27 Sequential measurements. An operator Ä, representing observ- able A, has two normalized eigenstates 1 and 2, with eigenvalues a1 and a2, respectively. Operator B, representing observable B, has two normalized eigen- states ø1 and ø2, with eigenvalues b1 and b2. The eigenstates are related by = (3ø1 + 402)/5, 42 = (401 – 302)/5. (a) Observable A is measured, and the value aj is obtained. What is the state of the system (immediately) after this measurement? (b) If B is now measured, what are the possible results, and what are their probabilities? (c) Right after the measurement of B, A is measured again. What is the proba- bility of getting a¡? (Note that the answer would be quite different if I had told you the outcome of the B measurement.)arrow_forward
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