(McQuarrie 4-22) Show that the following functions are orthonormal over the interval -x < x < ∞. These functions are the lowest eigenfunctions of the harmonic oscillator problem, which we will study in Chapter 5.) πT 1/4 40(x) = e-x²/2 4 1/4 41(x) = -x²/2 xe πT 42(x) = (+17) 14 (2x² - 1)e-²²/2 Hint: See the Table of Integrals handout for tips on integrating these even and odd functions. (McQuarrie 4-26) Prove that if 8nm is the Kronecker delta, then, 1 n = m бит = 0 nm Σιδη = Cm and Σanbmdnm = Σ ambn n=1 n=1 m=1 n These results will be used in various derivations. Hint: If you find this confusing, pick some particular value for m (e.g. m = 2) and then expand out the sums. Then see what the Kronecker delta does to each term in the sum.

(McQuarrie 4-22) Show that the following functions are orthonormal over the interval -x < x < ∞. These functions are the lowest eigenfunctions of the harmonic oscillator problem, which we will study in Chapter 5.) πT 1/4 40(x) = e-x²/2 4 1/4 41(x) = -x²/2 xe πT 42(x) = (+17) 14 (2x² - 1)e-²²/2 Hint: See the Table of Integrals handout for tips on integrating these even and odd functions. (McQuarrie 4-26) Prove that if 8nm is the Kronecker delta, then, 1 n = m бит = 0 nm Σιδη = Cm and Σanbmdnm = Σ ambn n=1 n=1 m=1 n These results will be used in various derivations. Hint: If you find this confusing, pick some particular value for m (e.g. m = 2) and then expand out the sums. Then see what the Kronecker delta does to each term in the sum.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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