Theoretical Physics 1 by Wolfgang Nolting

Author:Wolfgang Nolting
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Because of the linear independency of and this equation can only be fulfilled if A + = A − ∗ and A − = A + ∗ hold. So A + and A − are conjugate-complex quantities,

so that indeed we are left with only two independent parameters a and b. Inserted into (2.162) it follows:

The two types of solution (2.161) and (2.160) are therefore absolutely equivalent.

As general solution of a homogeneous differential equation of second order both (2.160) and (2.161) still contain two free parameters which must be fixed by initial conditions. We discuss two different situations: (a)At time t = 0 let the oscillator be displaced by x = x 0 and then released. That corresponds to the initial conditions:

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