A new approach to quantum mechanics

In my talk, I will discuss a reformulation of quantum mechanics in which each quantum system at any time is described by two Hilbert space vectors rather than one. One of the vectors propagates from past boundary condition towards the present and the other propagates back to the present from a future boundary condition. I will show that this reformulation uncovers a host of fascinating new physical phenomena and new mathematics. Examples of the former, i.e. new physical phenomena, are Weak Measurements and Weak Values. Examples of the latter, i.e. new mathematics, are superoscillations. Both examples will be described in detail within this talk.