Sunday, March 13, 2011

Mastering Physics: Normalizing the Wave Functions for the Harmonic Oscillator

The wave function for the ground state of the harmonic oscillator is
where C is an arbitrary constant, hbar is Planck's constant divided by 2\pi, m is the mass of the particle, \omega=\sqrt{k/m}, and k is the "spring constant" for the harmonic oscillator.

Part A
Normalize this wave function. What is the (positive) value of C once this wave function is normalized? You will need the formula
\int _{-\infty}^\infty e^{-ax^2}=\sqrt{\frac{\pi}{a}}.
Express your answer in terms of omega, m, hbar, and pi.

  C = \left(\frac{m{\omega}}{{\hbar}{\pi}}\right)^{\frac{1}{4}}

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