Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 3.2, Problem 3.3P
To determine

Show that if h|Q^h=Q^h|h for all h, then f|Q^g=Q^f|g.

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Show that if (h|ệh) = (Ôh\h) for all functions h (in Hilbert space), then (flÔg) = (Ôf\g) for all f and g (i.e., the two definitions of "hermi- tian"-Equations 3.16 and 3.17-are equivalent). Hint: First let h = f+ 8, and then let h = f + ig. (SIÊF) = (Ô ƒIS) for all f(x). [3.16] (FIÔg) = (Ô ƒ\g) for all f (x) and all g(x). [3.17]
Consider a rectangular surface of length L and width W in the xy plane with its center at the origin: Which of the following are valid expressions for the area vector of this surface? Check all that apply. O (0,0, LW) O (W, L, 0) O (0,0, -LW) O (LW, LW, 0) O (0, LW, 0) O (L, W, 0)
Let f(x, y) = x² + 4y² and let C be the line segment from (0, 0) to (2, 2). You are going to compute là Vf. dr two ways: first, using the method learned in section 6.2 for с evaluating line integrals, and second, using the fundamental theorem for line integrals. First way: Vf=( C can be parameterized by r(t) = (t, Then '(t) and ▼ ƒ(r(t)) = { so sv. So 2 = [² = 2 - 1² || ( Vf. dr ▼ f(r(t)). r' (t)dt dt ). > > for 0 ≤ t ≤ 2. ).
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