Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 3.6, Problem 3.24P
To determine
To show that if an operator
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For an operator to represent a physically observable property, it must be Hermitian, but need not be linear.
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function
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(a) Suppose that f(x) and g(x) are two eigenfunctions of an operator ĝ, with
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operator d2/dx2, with the same eigenvalue. Construct two linear combina-
tions of f and g that are orthogonal eigenfunctions on the interval (-1, 1).
Chapter 3 Solutions
Introduction To Quantum Mechanics
Ch. 3.1 - Prob. 3.1PCh. 3.1 - Prob. 3.2PCh. 3.2 - Prob. 3.3PCh. 3.2 - Prob. 3.4PCh. 3.2 - Prob. 3.5PCh. 3.2 - Prob. 3.6PCh. 3.3 - Prob. 3.7PCh. 3.3 - Prob. 3.8PCh. 3.3 - Prob. 3.9PCh. 3.3 - Prob. 3.10P
Ch. 3.4 - Prob. 3.11PCh. 3.4 - Prob. 3.12PCh. 3.4 - Prob. 3.13PCh. 3.5 - Prob. 3.14PCh. 3.5 - Prob. 3.15PCh. 3.5 - Prob. 3.16PCh. 3.5 - Prob. 3.17PCh. 3.5 - Prob. 3.18PCh. 3.5 - Prob. 3.19PCh. 3.5 - Prob. 3.20PCh. 3.5 - Prob. 3.21PCh. 3.5 - Prob. 3.22PCh. 3.6 - Prob. 3.23PCh. 3.6 - Prob. 3.24PCh. 3.6 - Prob. 3.25PCh. 3.6 - Prob. 3.26PCh. 3.6 - Prob. 3.27PCh. 3.6 - Prob. 3.28PCh. 3.6 - Prob. 3.29PCh. 3.6 - Prob. 3.30PCh. 3 - Prob. 3.31PCh. 3 - Prob. 3.32PCh. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - Prob. 3.35PCh. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - Prob. 3.40PCh. 3 - Prob. 3.41PCh. 3 - Prob. 3.42PCh. 3 - Prob. 3.43PCh. 3 - Prob. 3.44PCh. 3 - Prob. 3.45PCh. 3 - Prob. 3.47PCh. 3 - Prob. 3.48P
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- Suppose that you have three vectors: f1 (x) = 1, f2 (x) = x – 1, and f3 (x) = ; (x2 – 4x +2), that make up an orthonormal basis spanning the real vector space of quadratic functions with the inner product: (f; | f;) = S° fi (x) f; (x) e¯ªdx. Suppose we have a derivative operator D = . What is (Df1 | f3) =? %3D 6. dæ -1 3/4 Ооarrow_forwardLet o = (0;,,,0;), where o,,0,,0, are the Pauli matrices. If ā and b are two arbitrary constant vectors in three dimensions, the commutator [ā.6,6.6] is equal to (in the following I is the identity matrix) (a) (a-b)(0, +0, +0,) (b) 2i(āxb).ở (c) (ã-5)Iarrow_forwardIf A, B and C are Hermitian operators then 1 2i verfy whether the relation Hermitian or not. [AB] isarrow_forward
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