Answered: 1) Explain why any physically…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter28: Quantum Physics

Section: Chapter Questions

Problem 39P

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1) Explain why any physically realizable solution to the Schrodinger’s equation must be square-integrable.

2)The Chebyshev polynomials of the first kind can be otained from the recurrence relation, Tn+1(x) = 2xTn(x) −
Tn−1(x) with T0(x) = 1 and T1(x) = x.
a) Show that any two Chebyshev polynomials are orthogonal with respect to the weighting factor (1 − x
2
)
− 1
2 in
the closed interval [−1, 1].

b) Pick the first three Chebyshev polynomials and use Gram-Schmidt orthonormalization procedure to form an
orthonormal set in the closed interval [−1, 1].

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