A note on the Hilbert space formalism of quantum mechanics

Maciej Mączyński

Miklós Rédei

Sol Wieder

Sicong Jing, Bing-Sheng Lin

In deformation quantization, static Wigner functions obey functional *-genvalue equation, which is equivalent to time-independent Schrodinger equation in Hilbert space operator formalism of quantum mechanics. This equivalence is proved mostly for Hamiltonian with form Ĥ = (1/2)2 + V() [D. Fairlie, Proc. Camb. Phil. Soc. 60 (1964) 581]. In this note we generalize this proof to a very general Hamiltonian Ĥ(, ) and give examples to support it.

Carlo Franchetti

In this note we try to show that some a priori justifications can be given for the use of Hilbert spaces in Quantum Mechanics.

Y. B. Band, Y. Avishai