Quantum Mechanics - Introduction
Why do we need quantum mechanics?
Classical mechanics does not provide an accurate description of matter
on the scale of atoms and molecules. Electrons around a nucleus or nuclei
do not behave like planets orbiting the sun or like ping-pong balls bouncing
around in a container. Experiments show that when observing the properties
of very small bits of matter, such as a single electron, the matter exhibits
wave-like properties. Quantum mechanics is the mathematical description
of matter on the atomic scale.
In chemistry we are mostly interested in the electrons that give atoms
their properties and hold atoms together to form molecules. Thus to describe
matter, and to predict the properties of molecules, we must use quantum
The behavior of a quantum particle is completely described by the Schrödinger
operator - a series of mathematical steps.
- the operator that describes the energy of an electronic system.
wavefunction, y - a mathematical function that
describes a wave-like shape.
eigenvalue - a value obtained from operating on a wavefunction.
A given Hamiltonian operator will have a series of wavefunctions that
satisfy the Schrödinger equation. These wavefunctions are called eigenfunctions.
The Hamiltonian operating on the eigenfunctions produces the eigenvalues,
which are the allowed energies of the system.
For an illustration of how to use the Schrödinger equation see
the one-dimensional particle-in-a-box.
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