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Ideas of Quantum Chemistry P15

Ideas of Quantum Chemistry P15 shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. | 106 3. Beyond the Schrödinger Equation tems then the corresponding x t and x t satisfy the Lorentz transformation. It turns out that in both coordinate systems the distance of the event from the origin of the coordinate system is preserved. The square of the distance is calculated in a strange way as ct 2 - x2 for the event x ct . Indeed let us check carefully ct 2 - x 2 2 Vx ct-----------fx - Vct 1 - v2 c 1 - v2 c c2 c2 -----2 x2 c2t2 - 2vxt - x2 -1 - 4 Lc2 c2 V2 2 2 yc2 2 2vxt c2 -x2 c2t2 - x2 - -c212 ct 2 - x 2. 1 - L c2 c2 c2 3.29 3.30 There it is This equation enabled Hermann Minkowski to interpret the Lorentz transformation 3.28 as a rotation of the event x ct in the Minkowski space about the origin of the coordinate system since any rotation preserves the distance from the rotation axis . 3.1.8 HOW DO WE GET E mc2 The Schrodinger equation is invariant with respect to the Galilean transformation. Indeed the Hamiltonian contains the potential energy which depends on interparticle distances i.e. on the differences of the coordinates whereas the kinetic energy operator contains the second derivative operators which are invariant with respect to the Galilean transformation. Also since t t the time derivative in the time-dependent Schrodinger equation does not change. Unfortunately both Schrodinger equations time-independent and timedependent are not invariant with respect to the Lorentz transformation and therefore are illegal. As a result one cannot expect the Schrodinger equation to describe accurately objects that move with velocities comparable to the speed of light. Lecture 1965 Wheeler Feynman I know why all electrons have the same charge and the same mass F Why W Because they are all the same electron Then Wheeler explained suppose that the world lines which we were ordinarily considering before in time and space - instead of only going up in time were a tremendous knot and then when we cut through the knot by the plane corresponding to a fixed time we .