Question

My question relates to Example 2.4, Section 3 (The Harmonic Oscillator) in the textbook Introduction to Quantum Mechanics by DavidJ. Griffiths. My problem is with the normalization of of the following equation: |A|^2 \sqrt{\frac{m\omega}{\pi\hbar} (\frac{2m\omega}{\hbar})\int_{-infty}^\infty x^2 e^\frac{-m\omega x^2}{\hbar} dx.

Integration by parts does not work because e^(-x^2) is not a n elementary function. I tried using the technique of improper integral - type 1 infinite integral - but I was not able to obtain the normalization factor of 1 given in the textbook.

I would greatly appreciate having a detailed solution to find this normalizing constant.

Thank you for your kind attention.

Answer 1

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