What Parameter Should Be Used in Variational Approximation for This Hamiltonian?

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The discussion revolves around using variational approximation to estimate energy for a specific Hamiltonian, bx^4 + p²/2m. The initial suggestion is to use the ground state wave function of the harmonic oscillator, but uncertainty exists about which parameter to vary. Participants propose varying the product mω/ħ as a potential parameter for optimization. There is skepticism about the effectiveness of the harmonic wave function in this context. The conversation highlights the need for clarity on parameter selection in variational methods.
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Hello. I should find the energy aproximatelly using the variational approximation for this physical hamiltonian: ##bx^4 + p²/2m## Imediatally, i thought that the better trial wave function would be the one correspondent to the ground state of the harmonic quantum oscilator. THe problem is, in fact, that i don't know what parameter to use in order to vary it! I mean, $$\psi = (mw/\pi \hbar)^{1/4}e^{-mwx^2/2 \hbar}$$. So, what parameter should i use? w=w(\alpha)? or m = m(\alpha)? How do i know by the beginning what parameter should i use to vary it?
 
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