Find wavefunction of harmonic oscillator

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Homework Help Overview

The discussion revolves around finding the wavefunction of a harmonic oscillator given specific conditions regarding energy and probability measurements. The subject area is quantum mechanics, specifically focusing on the properties of harmonic oscillators and their wavefunctions.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the implications of the given energy condition, questioning whether it represents an eigenstate or an average energy. There is discussion about the probability of measuring energy above a certain threshold and how it relates to the coefficients of the wavefunction. The role of symmetry and parity in determining the average position is also examined.

Discussion Status

The discussion is ongoing, with participants providing insights and questioning each other's reasoning. Some guidance has been offered regarding the nature of the wavefunction and its symmetry properties, but no consensus has been reached on the specific form of the wavefunction or how to proceed with the conditions given.

Contextual Notes

Participants note the constraints of the problem, including the lack of explicit definitions for the wavefunction and the ambiguity surrounding the energy condition. There is also mention of the need to consider both the first and second conditions when determining the wavefunction.

  • #31
ah right. I understand you now. If we make the total wavefunction ##\psi## either symmetric or anti-symmetric, then we are guaranteed that ##\langle x \rangle## is zero. And we know the mod square of the energy eigenstates are symmetric. Therefore, we can guarantee ##\langle x \rangle = 0## by getting rid of the cross terms.
 

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