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What is Ab Initio Calculations about?

Various difficulties of classical physics, including inadequate description of atoms and molecules, led to new ways of visualizing physical realities, ways which are embodied in the methods of quantum mechanics. Quantum mechanics is based on the description of particle motion by a wave function, satisfying the Schrodinger equation, which in its “time-independent” form is: ((−h2/8mπ2)⛛2+V)Ψ=E Ψ or, for short: HΨ = EΨ In this equation, H, the Hamiltonian operator, is defined by H = − ((h2/8mπ2)⛛2+V, where h is Planck’s constant (6.6 10−34 Joules), m is the particle’s mass, ⛛2 is the sum of the partial second derivative with x,y, and z, and V is the potential energy of the system. As such, the Hamiltonian operator is the sum of the kinetic energy operator and the potential energy operator. (Recall that an operator is a mathematical expression which manipulates the function that follows it in a certain way. For example, the operator d/dx placed before a function differentiates that function with respect to x.) E represents the total energy of the system and is a number, not an operator. It contains all the information within the limits of the Heisenberg uncertainty principle, which sta

Author

Anne-Marie Sapse

Publisher

Oxford University Press

Published

1998

Language

EN