L13.3 The harmonic oscillator: analytic method solution

#harmonicoscillator #analyticmethod #quantummechanics
0:00 using power series solution method
3:36 recursion relation
4:15 odd and even coefficients
7:44 normalizable solutions
8:50 limiting the value of j
11:34 value of k
12:10 energy of the nth state

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2.3.2 The harmonic oscillator: analytic method solution
A harmonic oscillator (quantum or classical) is a particle in a potential energy well given by V(x)=½kx². k is called the force constant. It can be seen as the motion of a small mass attached to a string, or a particle oscillating in a well shaped as a parabola. This is a very important model because most potential energies can be approximated as parabolas near their minima, and the model allows us to understand the vibrations in molecular systems.