Question:
How to construct another wave-function from one such that it overall gain a negative sign in the Dirac equation?
Solution:
The Dirac equation is:
$ i\hbar{\frac{\partial \Psi}{\partial t}} = (\hat{\alpha}\hat{p} + mc^2\hat{\beta})\Psi $.
We know $ \{\alpha, \beta\} = \alpha\beta + \beta\alpha = 0 $, so we have $\alpha\beta = -\beta\alpha $, that how a negative sign is introduced.
So all we need to do to make sure it gain an overall negative sign is simply make sure we have odd number of $\alpha \beta $.
That explains the existence of anti matter!
How to construct another wave-function from one such that it overall gain a negative sign in the Dirac equation?
Solution:
The Dirac equation is:
$ i\hbar{\frac{\partial \Psi}{\partial t}} = (\hat{\alpha}\hat{p} + mc^2\hat{\beta})\Psi $.
We know $ \{\alpha, \beta\} = \alpha\beta + \beta\alpha = 0 $, so we have $\alpha\beta = -\beta\alpha $, that how a negative sign is introduced.
So all we need to do to make sure it gain an overall negative sign is simply make sure we have odd number of $\alpha \beta $.
That explains the existence of anti matter!
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