The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal’s approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.

It is shown that, for a harmonic oscillator in the ground state, Bohmian mechanics and quantum mechanics predict values of opposite sign for certain time correlations.

Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through the requirement of an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations acting on the position and momentum uncertainties are induced by isotropic space dilatations. This invariance imposes a change in the laws of cl...

Understanding how a solvent affects the quantum mechanics and reactivity of the chemical bonds of dissolved solutes is of fundamental importance to chemistry. To explore condensed-phase effects on a simplemolecular solute, we have studied the six-dimensional two-electron wave function of the bonding electrons of the Na2 molecule in liquid argon via mixed quantum/classical simulation. We find th...

Relational Quantum Mechanics (RQM) claims to be an interpretation of quantum theory [see arXiv:2109.09170, which appears in the Oxford Handbook History Interpretation Physics]. However, there are significant departures from theory: (i) RQM measurement outcomes arise interactions entangle a system $S$ and observer $A$ without decoherence, (ii) such outcome is "fact" relative $A$, but it not fact...

Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in ...

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under...

I argue that the logical difference between classical and quantum mechanics that Stapp (1995) claims shows quantum mechanics is more amenable to an account of consciousness than is classical mechanics is irrelevant to the problem.