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Thread: Question about Dirac equation?

  1. #1 Question about Dirac equation? 
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    The solution of the Dirac equation is of the form ue^(i(px-Et)) with u the vector part. If the probability density is the complex conjugate of the solution multiplied by the solution, and e^i*e^-i always equals one, so won't the probability density come out to be a scalar constant?
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  2. #2  
    mvb
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    Quote Originally Posted by muon321 View Post
    The solution of the Dirac equation is of the form ue^(i(px-Et)) with u the vector part. If the probability density is the complex conjugate of the solution multiplied by the solution, and e^i*e^-i always equals one, so won't the probability density come out to be a scalar constant?
    The answer is basically "yes, but ...." The solutions you have quoted are the plane-wave solutions in the absence of interactions. A general solution can, as usual for differential equations, be written as the linear combination of any number of the plane-wave solutions [a1u1 + .a2u2+...]. Then when you take the product that gives you the probability density the cross-products of different solutions [say a1*a2u1*u2 ] give you non-constant functional forms.
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