Question: The potential function of a one-dimensional oscillator of mass m and angular frequency is V(x) = kx 2 + cx 4 Where the

The potential function of a one-dimensional oscillator of mass m and angular frequency ω is

V(x) = ½ kx ² + cx ⁴

Where the second term is small compared to the first.

a. Show that, to first order, the effect of the anharmonic term is to shift the energy E ₀ of the ground state by 3c(h/2m ω) ².

b. What would be the first-order effect on the energy of an additional term in x ³ in the potential?

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