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Homework Help
Precalculus Mathematics Homework Help
Completing the Square Homework Statement
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[QUOTE="denjay, post: 4546618, member: 419616"] [h2]Homework Statement [/h2] Consider a charged particle of mass m in a harmonic potential and in the presence also of an external electric field E = E[itex]\hat{i}[/itex]. The potential for this problem is simply V(x) = 1/2 mw[itex]^{2}[/itex]x[itex]^{2}[/itex] - qεx where q is the charge of the particle. 1) Show that a simple change of variables turns this problem into one of a particle under only a harmonic oscillator potential. (Hint: Complete the square.) [h2]Homework Equations[/h2] (ax-b)[itex]^{2}[/itex] = a[itex]^{2}[/itex]x[itex]^{2}[/itex] - 2abx + b[itex]^{2}[/itex] [h2]The Attempt at a Solution[/h2] So I know the way to simplify the potential is by completing the square. I only know the way of completing the square when a quadratic equation is equal to 0 but in this case it's a function. So with that formula for (ax-b)[itex]^{2}[/itex] I believe 1/2 mw[itex]^{2}[/itex] is a[itex]^{2}[/itex] and -2ab is -qε but I'm unsure. So what I got was that b = qε/(2mw[itex]^{2}[/itex]) so the equation is V(x) = 1/2 mw[itex]^{2}[/itex]x[itex]^{2}[/itex] - qεx + q[itex]^{2}[/itex]ε[itex]^{2}[/itex]/2m[itex]w^{2}[/itex] - q[itex]^{2}[/itex]ε[itex]^{2}[/itex]/2m[itex]w^{2}[/itex] = ([itex]\sqrt{1/2 mw^{2}}x[/itex] - qε/[itex]\sqrt{2mw^2}[/itex])^2 - q[itex]^{2}[/itex]ε[itex]^{2}[/itex]/2m[itex]w^{2}[/itex] [/QUOTE]
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Precalculus Mathematics Homework Help
Completing the Square Homework Statement
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