An elementary proof for the non-bijective version of Wigner%26apos;s theorem

作者：Geher Gy P^*

来源：Physics Letters, Section A: General, Atomic and Solid State Physics , 2014, 378(30-31): 2054-2057.

DOI：10.1016/j.physleta.2014.05.039

• Wigner%26apos
• s theorem
• Quantum mechanical symmetry transformation
• Linear and antilinear isometries
• Resolving set

The non-bijective version of Wigner%26apos;s theorem states that a map which is defined on the set of self-adjoint, rank-one projections (or pure states) of a complex Hilbert space and which preserves the transition probability between any two elements, is induced by a linear or antilinear isometry. We present a completely new, elementary and very short proof of this famous theorem which is very important in quantum mechanics. We do not assume bijectivity of the mapping or separability of the underlying space like in many other proofs.

• 出版日期2014-6-13