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I just need to know. Why exactly what's the complex number i=√–1 put in the wave function for matter. Couldn't it have just been exp(kx–wt)?
It's not possible to normalize that kind of a real-valued exponential function. The Schroedinger equation is a complex diffusion equation, and the complex numbers make it possible to obtain wave-like behavior (wavepackets reflecting from walls, etc.) instead of the simple dissipative dynamics of ordinary diffusion where the solution is a real function.I just need to know. Why exactly what's the complex number i=√–1 put in the wave function for matter. Couldn't it have just been exp(kx–wt)?
Sure, you can have parts of the wavefunction look like exp(kx-wt), but not the whole thing. If you consider a WKB approximation for the time independent Schrodinger equation, you get solutions that look likeI just need to know. Why exactly what's the complex number i=√–1 put in the wave function for matter. Couldn't it have just been exp(kx–wt)?