Probability densities for the electron of a hydrogen atom in different quantum states. (ref: http://en.wikipedia.org/wiki/Quantum_state)

Some trajectories of a harmonic oscillator (i.e. a ball attached to a spring) in classical mechanics (A-B) and quantum mechanics (C-H). In quantum mechanics, the position of the ball is represented by a wave (called the wave function), with the real part shown in blue and the imaginary part shown in red. Some of the trajectories (such as C,D,E,and F) are standing waves (or "stationary states").

Does the quantum wave function represent reality? (Phys.org) -- At the heart of quantum mechanics lies the wave function, a probability function used by physicists to understand the nanoscale world. Using the wave function, physicists can calculate a system's future behavior, but only with a certain probability. This inherently probabilistic nature of quantum theory differs from the certainty with which scientists can describe the classical world, leading to a nearly century-long...

http://www.facebook.com/ScienceReason ... Quantum Mechanics (Chapter 3): Wave Function and Wave-Particle Duality. --- Please SUBSCRIBE to Science & Reason: • http://www.youtube.com/Best0fScience • http://www.youtube.com/ScienceTV • http://www.youtube.com/FFreeThinker --- 1. A Brief History Of Quantum Mechanics http://www.youtube.com/watch?v=B7...

This kaleidoscopic image is a wave function, illustrating the locational probabilities of an excited subatomic particle. The particle is more likely to be in the red areas than in the green; it is least likely to be in the black spaces. Using other particles or magnetic and electric fields, the area can be manipulated into different shapes, in this case, a heartlike shape called a cardioid.

Scott Aaronson Many Worlds of Quantum Theory (Closer to Truth) - YouTube