Quantum Mechanics: 1D Parabolic Potential Wave Function

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SUMMARY

The discussion centers on the wave function for a 1D harmonic oscillator in Quantum Mechanics, specifically addressing the need to state the wave function for n=0 and n=1. Participants clarify that the question requires a linear combination of eigenfunctions multiplied by a time factor, emphasizing the importance of time dependence in the solution. The focus is on understanding the wave function's formulation without needing to prove it, which is crucial for exam preparation.

PREREQUISITES
  • Understanding of Quantum Mechanics principles
  • Familiarity with 1D harmonic oscillator concepts
  • Knowledge of wave functions and eigenfunctions
  • Basic grasp of time-dependent Schrödinger equation
NEXT STEPS
  • Study the derivation of the wave function for the 1D harmonic oscillator
  • Learn about linear combinations of eigenfunctions in Quantum Mechanics
  • Explore time-dependent solutions in Quantum Mechanics
  • Practice probability calculations related to wave functions
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Students preparing for Quantum Mechanics exams, educators teaching Quantum Mechanics concepts, and anyone interested in the mathematical formulation of wave functions in quantum systems.

dcuk86
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Hi, I'm currently working through some exam papers from previous years before an upcoming module in Quantum Mechanics.
I'm a little stumped with this one, I'm assuming that I'm looking at a 1D harmonic Oscillator and the wording of the question suggests that the wave function just needs to be stated and not actually proven (?).
In your opinion is this question looking for the wavefunction for n=1 or a general wavefunction in terms of n? its mostly the time dependence which has thrown me.
 

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apologies, I'm fairly new to this forum, I think I should have posted this in the homework section?
 
Well, you have to write down a linear combination of eigenfunctions for a case n=0 and n=1, and then multiply it by a time factor. And then do a probability problem.

That is how I would do it.
 
thanks for that, I'll give it a go and let you know how I get on
 

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