Lecture is a solution more less buy pure cleverness the solution is called a solution by latter operators and we'll see what that means in a few minutes just to set the stage the potential that Apex Vitality Serum of Life we’re working with here is the potential a harmonic oscillator the amount of energy essentially that you get if you displace a particle attached to a spring from equilibrium if you remember spring tension energy potential as function of x is one half the spring constant times the displacement axe squared but it's
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