At the moment I am studying the Schrodinger equation using this resource.(adsbygoogle = window.adsbygoogle || []).push({});

In a 1D solution (sec 3.1 in the paper) they show that a wave function can be expressed as

[tex]\Psi(x,t)=\sqrt{2}e^{-iE_{n_x}t}\sin (n_x\pi x)[/tex]

where n_x is the quantum number. And they show the real part of the solution in Figure 2a for t=0 and for over time in Figure 3a. I do not understand the structure seen in the time-dependent solution. In particular, in my solution I can show exactly what they give in Figure 3 except that I ONLY show the wavefunction being positive at x<0.5 and negative in x>0.5. I can only get all their curves if I assume that the wave function is both positive and negative over time.

I think this might be due to the fact that I do not understand the use of the imaginary number in the equation and solutions. For instance, apparently when the above equation is squared you arrive at

[tex]\Psi^2=2\sin^2 (n_x\pi x)[/tex]

But I don't see how that operates on the exponential. So what is the function of the imaginary number in the schrodinger equation? Do you just assume that i=1 sometimes and i=-1 othertimes?

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# Imaginary numbers and the real part of the Schrodinger Equation

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