‘Heisenberg Picture’ of Quantum Mechanics Without Born Rule or “Uncertainty Principle”

F. J. Duarte

The essence of quantum mechanics involves indistinguishability , superposition , Heisenberg's uncertainty principle , nonlocality of the photon , and Born's rule . As a whole, these concepts integrate the indeterminacy of quantum mechanics. Indistinguishability and superposition are quantum concepts that together with probability amplitudes are crucial coherent concepts that are part of the first layer of quantum mechanics. Albeit functioning at the mathematical unmeasurable realm of quantum physics, these concepts, nevertheless, faithfully reflect the reality of experimental configurations. Heisenberg's uncertainty principle, nonlocality of the photon, and Born's rule manifest themselves in the second layer of quantum mechanics: the measurable realm . Here, all these five concepts are considered from the experimentalist's perspective. This chapter concludes with the observation that the essence of quantum mechanics is closely and intrinsically entangled with the ethos of physics: the experiment .

Daniel R. Bes

Maurice A. de Gosson

The aim of this short Note is to show that the Schrödinger and Heisenberg pictures of quantum mechanics are not equivalent unless one uses a quantization rule clearly stated by Born and Jordan in their famous 1925 paper. This rule is sufficient and necessary to ensure energy conservation in Heisenberg's matrix mechanics. It follows, in particular, that Schrödinger and Heisenberg mechanics are not equivalent if one quantizes observables using the Weyl prescription.

Daniel R. Bes

de Gosson, Anthony Maurice

The aim of this short Note is to show that the Schrodinger and Heisenberg pictures of quantum mechanics cannot be equivalent unless one uses a quantization rule clearly stated by Born and Jordan in their famous 1925 paper. This rule is sufficient and necessary to ensure energy conservation in Heisenberg's matrix mechanics. It follows, in particular, that Schrodinger and Heisenberg mechanics yield different theories if one quantizes the Hamiltonian using the Weyl prescription.