Quantum harmonic oscillators DE wavefunction

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SUMMARY

The discussion centers on the differential equation for the zeroth wavefunction of a quantum harmonic oscillator. The user has derived a solution that differs by a constant from the expected result found in their textbook. The equation involves variables related to mass, frequency, and Planck's constant, indicating a focus on quantum mechanics principles. The user seeks clarification on their approach and the discrepancies between their solution and the textbook's answer.

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  • Understanding of quantum mechanics principles, specifically harmonic oscillators.
  • Familiarity with differential equations and their applications in physics.
  • Knowledge of Planck's constant and its role in quantum mechanics.
  • Basic proficiency in LaTeX for formatting equations in discussions.
NEXT STEPS
  • Review the derivation of the zeroth wavefunction for quantum harmonic oscillators.
  • Study the impact of constants in quantum mechanical solutions.
  • Learn how to properly format equations using LaTeX for clarity in discussions.
  • Explore common discrepancies in solutions between textbooks and individual derivations in quantum mechanics.
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Students and researchers in quantum mechanics, particularly those studying harmonic oscillators and seeking to understand common pitfalls in solving differential equations.

moriheru
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My question concerns a really simple differential equation for the zeroth wavefunction of a harmonic oscillator.
I have pretty much got it but my solution just differs by a constant,so I thought why think when one can ask other people :). Here is the equation:

Snapshot.jpg


Where the x star represent a variable involving mass frequency and Plancks constant. There is a psi function missing in the second equation (for any latex tips please e-mail me)
(Posted to early so there was no equation on the original post;had to edit it)
 
Last edited:
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Sorry Latex is wrong change it in a minute. So here it is.
 
Last edited:
Is should specify: the above is my solution and my question is what I did wrong as my book has a different solution.
Thanks for any help.
 

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