Who can solve the probability of perturbation in simple harmonic oscillator

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SUMMARY

The discussion centers on solving the probability of perturbation in a simple harmonic oscillator, specifically focusing on deriving the perturbed wavefunction in the ground state. The user seeks clarification on finding the normalization constant \( N \) and the parameter \( \alpha \) related to the wavefunction. The conversation emphasizes the need for a clear expression for the perturbed wavefunction to accurately calculate the probability of the system's state. The user expresses uncertainty but is eager for a definitive solution to question d) and insights on part (i).

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly simple harmonic oscillators.
  • Familiarity with perturbation theory in quantum mechanics.
  • Knowledge of wavefunction normalization techniques.
  • Basic proficiency in mathematical expressions related to quantum states.
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  • Research the derivation of perturbed wavefunctions in quantum mechanics.
  • Study normalization methods for wavefunctions in quantum systems.
  • Explore perturbation theory applications in simple harmonic oscillators.
  • Investigate the calculation of probabilities from wavefunctions in quantum mechanics.
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Students and researchers in quantum mechanics, particularly those focusing on perturbation theory and wavefunction analysis in simple harmonic oscillators.

Youngwoo
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Pleae help me.
a),b),c) was already solved.
but question d) is not.
 

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I'm not 100% sure but maybe you have to find an expression for the perturbed wavefunction in the ground state and then use this to find the probability? Again, that is just my intuition, I may be completely wrong, but I'd be interested to see a solution.

Also just out of interest how did you do part (i)? I assume you use normalisation to find N, but how do you find alpha?
 
Tangent87 said:
I'm not 100% sure but maybe you have to find an expression for the perturbed wavefunction in the ground state and then use this to find the probability? Again, that is just my intuition, I may be completely wrong, but I'd be interested to see a solution.

Also just out of interest how did you do part (i)? I assume you use normalisation to find N, but how do you find alpha?

I attached my solution
 

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