Quantum Chemistry 5.9 - Even and Odd Functions

Short lecture on even and odd functions.

Even functions are those which are symmetric with respect to refelction across the y-axis, such that f(x) = f(-x). Odd functions are those which are symmetric with respect to inversion through the origin, such that f(x) = -f(-x). Any function can be decomposed into its even and odd components. The integral over all space of an even function is twice its integral from zero to infinity. The integral over all space of an odd function is zero. Even functions include even order polynomials, cosine, and Gaussian functions. Odd functions include odd order polynomils and sine function.

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[TMPChem]

Notes and Corrections:

5:32 Cosine is an even function, and sine is an odd function. I should be taking the derivative of sine instead of cosine. The result is correct, but the functions used have the opposite evenness / oddness relative to the label.

[curlymeg]

Thank you for these videos. These are helping me so much.

[nkyu]

in the last part of the note, it seems sin(kx) should be inside 'd()/dx'.