Why are wave functions, e.g., Schrodinger's, based on the complex exponential function (e[tex]^{}ix[/tex]) and not trigonometric functions (sine or cosine)?(adsbygoogle = window.adsbygoogle || []).push({});

See Euler's formula for their relationship: http://en.wikipedia.org/wiki/Euler's_formula

Furthermore, by using the complex exponential function, the probability amplitude becomes a complex-valued function (a + bi). Were sine or cosine used, the probability amplitude of the wave function would not be a complex-valued function. Is there a reason that the probability amplitude should be a complex-valued function?

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# Wave functions

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