Let's consider the d'Alembert's solution
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(1) |
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(2) |
We expand the given function
to the Fourier sine series on the interval
:
Thus we may write
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(3) |
Note. The solution (3) of the wave equation is especially simple in the special case where one has besides (2) the sine-formed initial condition
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(4) |
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(5) |
Remark. In the case of quantum systems one has Schrödinger's wave equation whose solutions are different from the above.
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