Complex or real wave function?
It is not clear what complex wave function means in Schrödinger, Pauli, Dirac equations. Is it always two-component (complex), or can it be real, or are both variants possible in different situations?
For example, how to understand:
-i · h/(2·π) · ∂ψ/∂t = h2/(8·π2·m) · div grad ψ
(for simplicity in absence of potential multiplied by function).
The imaginary unit “i” simply shows that quantum operator is used instead of classical derivative, or function must be divided into tw
You're absolutely right. +1. An image is worth a thousand words:
The image is not mine, of course. It's from Wikipedia, and it represents the time evolution of a free quantum-mechanical wave packet. You can actually see how dispersive the non-relativistic regime is. The low-down is: Even empty space somehow operates as a dispersive medium for Schrödinger waves.
Although you can get a similar behaviour for waves that are actually waves --same order in time and space derivatives--
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