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 4.1, Problem 4.1P

(a)

To determine

Compute commutation relations of components of position and momentum operators.

(b)

To determine

Confirm the three-dimensional version of Ehrenfest’s theorem.

(c)

To determine

Formulate Heisenberg’s uncertainty principle in three dimensions.

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(a) Suppose that f(x) and g(x) are two eigenfunctions of an operator ĝ, with the same eigenvalue q. Show that any linear combination of f and g is itself an eigenfunction of Q. with eigenvalue q. (b) Check that f (x) = exp(x) and g(x) = exp(-x) are eigenfunctions of the 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).
Suppose I have an operator A, and I discover that Â(2²) = 5 sinx and Â(sin x) = 5x². (a) Find Â(2² - sin x) (b) Name one eigenfunction and one eigenvalue of A.
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