Talk:Making sense of quantum mechanics/Principles of Quantum Mechanics

Quantum probabilities principle
This (fifth) principle needs to be much more worked out. I am not really satisfied with the header "Quantum probabilities involve interaction cross sections of both observed and observing particles". I intended to say that probabilities are given be square wavefunction amplitudes (Borns probability interpretation), because both observed and observing particle are subjected to the same pilot wavefunction, which gives probabilities of the kind $$|\psi^2|$$. This probability principle is therefore a corollary of a more fundamental principle, which is rarely mentioned as such: the phase of the particles are steered by the phase of a pilot wave (de Broglie's or Bohm's principle). This principle is suggested by the figure of the arrow bouncing back and forth in the box: even if the walls weren't there, the arrow-particle would rotate in phase with the wave. Arjen Dijksman 19:48, 21 October 2007 (UTC)

Generalized Schroedinger equation
I propose a generalized Schrödinger equation which is, as far as I see, the most general form of the central quantum evolution law. This equation is valid for any vector-like object (macroscopic or microscopic). It may be deduced directly from the geometrical consideration of the following figures. Starting from an arbitrary vector $$|\psi \rangle$$, we subtract it from the rotated vector $$e^{i{\Delta \phi}}.|\psi\rangle$$, giving the little vector $$\Delta |\psi \rangle$$. If we draw the vector $$i |\psi \rangle$$ and multiply it by the amount $$\Delta \phi$$, we obtain an equivalent vector $$\Delta \phi. i |\psi \rangle$$ for $$\Delta \phi$$ going to 0. This gives the equation: $$i |\psi \rangle d \phi = d |\psi \rangle$$

Considering that $$d \phi$$ = $$\omega dt + t d\omega$$ or $$k dx + x dk$$ depending on the variables you choose, specialized Schroedinger equations may be obtained. Arjen Dijksman 18:45, 20 November 2007 (UTC)