?Write the normalized form of the ground state wavefunction of the harmonic oscillator
Chapter 7, Problem P7E.10(choose chapter or problem)
Write the normalized form of the ground state wavefunction of the harmonic oscillator in terms of the variable y and the parameter \(\alpha\). (a) Write the integral you would need to evaluate to find the mean displacement \(\langle y\rangle\), and then use a symmetry argument to explain why this integral is equal to 0. (b) Calculate \(\left\langle y^{2}\right\rangle\) (the necessary integral will be found in the Resource section). (c) Repeat the process for the first excited state.
Text Transcription:
left angle y right angle
alpha
left angle y^2 right angle
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