Question: Show that [ Ae ikx + Be -ikx ] and [ C cos kx + D sin kx ] are equivalent ways of writing the

Show that [ Ae^ikx + Be^-ikx ] and [ C cos kx + D sin kx ] are equivalent ways of writing the same function of x, and determine the constants C and D in terms of A and B, and vice versa. Comment: In quantum mechanics, when V = 0, the exponential represent travelling waves, and are most convenient in discussing the free particle, whereas sines and cosines correspond to standing waves , which arise naturally in the case of the infinite square well.

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