Finding Ground State Wave Functions: Tips & Tricks

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SUMMARY

The discussion focuses on finding the ground state wave functions, ψ(x), for the Hamiltonian H=(1/2)p²+(1/24)λ(x²-v²)². Participants suggest utilizing techniques such as clever variable changes and perturbation theory, drawing parallels to the harmonic oscillator model. Additionally, they recommend searching for "high order expansion anharmonic oscillator" on Google Scholar for further references and insights into the topic.

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LAHLH
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Hi,

If I have the Hamiltonian: [itex]H=(1/2)p^2+(1/24)\lambda(x^2-v^2)^2[/itex] what is the best way to find the ground state wave functions [itex]\psi(x)[/itex]. I was thinking this sort of looks like the harmonic osscilator, so maybe a clever change of variables could do the trick? or some form of perturbation perspective?
 
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LAHLH said:
Hi,

If I have the Hamiltonian: [itex]H=(1/2)p^2+(1/24)\lambda(x^2-v^2)^2[/itex] what is the best way to find the ground state wave functions [itex]\psi(x)[/itex]. I was thinking this sort of looks like the harmonic osscilator, so maybe a clever change of variables could do the trick? or some form of perturbation perspective?
Enter the key words
high order expansion anharmonic oscillator
into http://scholar.google.com to get a lot of references.
 
A. Neumaier said:
Enter the key words
high order expansion anharmonic oscillator
into http://scholar.google.com to get a lot of references.

thanks, will check those out.
 

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