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Find the normalization constants for the two wave functions

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Reference no: EM131026912

Use Gaussian multiplication on the Hermite polynomials in the attached document. These give the un-normalized wave functions for the levels of the harmonic oscillator.

The 3rd and 4th Hermite polynomials are, respectively:

H_2(x) = 4x^2 - 2

H_3(x) = 8x^3 - 12x

When multiplies by the Gaussian, e^-ax^2 /2 (please see the attached file), these give the un-normalized wave functions for the v = 2 and 3 levels of the quantum harmonic oscillator.

a. Show that the resulting wave functions are orthogonal to each other.

b. Find the normalization constants for the two wave functions.

Reference no: EM131026912

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