A field theoretic derivation of the Max Born hypothesis
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Abstract: (AIP)
It is shown in this article that the statistical character of the nonrelativistic, one particle quantum probabilities can be inferred from the function which results from the Wigner transformation on the field operator ψ ̂ † ( x ⃗ ) which, in turn, must be expressed in the occupation number representation. The function which results from the Wigner transformation is shown to be the state function of a single particle which is defined in the conventional quantum mechanics. The integral of the norm squared of that function is proven to be unity which is the step that proves the Max Born hypothesis. The compatibility of the expression for the field amplitude, obtained here, with the measurability of the Bosonic and the Fermionic fields is explained.- 02.30.Uu
- 03.65.Yz
- 02.30.Tb
- 05.30.-d
- quantum statistical mechanics
- transforms
- mathematical operators
- particle: nonrelativistic
- statistical mechanics
- field theory
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