Quantum Intro

Quantum Intro - INTRODUCTION TO QUANTUM CHEMISTRY Problems...

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Quantum Intro 1 INTRODUCTION TO QUANTUM CHEMISTRY Problems with classical mechanics OBJECTIVES : To show •how classical mechanics failed to explain microscopic properties •the foundations of quantum mechanics •basic applications of quantum mechanics, particularly in computational chemistry and spectroscopy 1953 - Louis de Broglie about the revolution in Physics: "Despite the importance and the extent of the progress accomplished by physics in the last centuries, as long as the physicists were unaware of the existence of quanta , they were unable to comprehend anything of the profound nature of physical phenomena for, without quanta , there would be neither light nor matter." Richard Feynman: Things on a very small scale behave like nothing you have any direct experience about. They do not behave like waves, they do not behave like particles, they do not behave like clouds, billiard balls, weights or springs, or like anything that you have seen. THREE CONCEPTS: QUANTUM, DUALITY, UNCERTAINTY
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Quantum Intro 2 Difficulties: Our experience confirms the classical view. The new physics deals with "uncertainty" and "probability" and "indeterminacy" to understand things that we cannot directly observe. The new physics is "inherently" mathematical. Math is not a "tool" but the "language". Since observing modifies, the new physics will deal with a "subjective" universe. The events are "acausal". One will only be able to predict the "probability" of an event within a system with large number of elements.
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Quantum Intro 3 Historical overview. 1900: mechanics and electromagnetism. Classical mechanics 1. In absence of external forces, the total energy is constant. Total energy: E = E k + V(x) Kinetic arising from motion p (linear momentum) = mv Potential arising from the position in a field of force Potential energy defined from force: F (vector); the direction of the force toward decreasing potential energy Total energy: If no force, then E=E k Else: Note: p (vector), v (vector), p 2 (scalar), energy (scalar) dx dV F V(x) 2m p E 2 p mv ½ E 2 2 k Knowing the location of a body, its momentum (mass and velocity), and the forces acting on it, is sufficient to predict its location and momentum at any future time . 2. The rate of change of momentum is equal to the force acting on the body: (the rate of change of velocity is the acceleration) Consequence: dt dp dv m m F
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Quantum Intro 4 Electricity & Magnetism 1. Important relationships: Coulomb's law: F = 8.9876 x 10 9 (F in N, q in C, r in m) if q = electron charge; F = ( 0 is the permittivity of vacuum) F = f q (F in N; field strength in Volts per m; q in C) F = - (potential energy gradient; J/m) E = V AB q (E in J; V or electrical potential in Volts; q in C) P = V AB I (Power in watts; watts in J/s; current I in Amperes or C per second) Lenz's law: F = q v X B [v in m/s; magnetic flux in teslas (T); vectorial product (sin) ] Electrical, magnetic and mechanical energy are interconvertible 2 2 1 r q q 0 2 2 4 r Ze x V 2. The nature of light - two opposing concepts: Newton - corpuscular theory Huyghens - wave theory Newton's argument: a prism refracts different colors at different angles.
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Quantum Intro - INTRODUCTION TO QUANTUM CHEMISTRY Problems...

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