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Mike, What Is You Math Background?

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Posted by Alexander on July 11, 2001 16:22:32 UTC

You seem not to understamd simple mathematical objects like infinite line.

Imaginary numbers make direct physical sense. Consider a quantum particle in a box with thick walls. Solution of Shredinger equation for it (amplitude of probability to find it - wave function, or psi-function) has the form of exp(ikx) +exp(-ikx), where k =p/h = sqrt(2m(E-U))/h. So, if particle's energy is more than the potential energy U, k is real and (ikx) thus is IMAGINARY number. As you said, "made up" number which does not apply in real life. Ooops! But the sum of the exponents of imaginary numbers is REAL function sin(kx) and it exactly represents WAVE motion of the particle inside the box. Now let's see what is going on when a particle passes inside the box WALL. There we have a situation EU egein and the particle again turns into a wave - exactly as imaginary numbers require.

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