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[tex] \frac{\d^2\psi}{dx^2} = - \frac{2mE}{\hbar^2}\psi [/tex]

Solving to find that

[tex] \psi = Aexp(ikx)+Bexp(-ikx) [/tex]

I am curious about the physical meanings of the two terms of the solutions.

In solving a free particle encountering a potential barrier, In the region before the encounter of the barrier, the solutions of the Shcrodinger equation is just the free particle equation above. My teacher says the term with the positive sign means it's a wave going towards the barrier, whereas the negative signs is the wave that reflect from it.

Well, the wave function is just the solution of the Schrodinger's equation and how does my teacher derives the physical meaning from it?? I mean the exponential function has complex term, which are actually sinusoidal but doesn't tell us anything about the direction of going??