# Wave Function And WaveParticle Duality

Wave Function

A wave function or wavefunction is a mathematical tool used in quantum mechanics to describe any physical system. It is a function from a space that maps the possible states of the system into the complex numbers. The laws of quantum mechanics (i.e. the Schrödinger equation) describe how the wave function evolves over time.

The values of the wave function are probability amplitudes — complex numbers — the squares of the absolute values of which give the probability distribution that the system will be in any of the possible states.

It is commonly applied as a property of particles relating to their wave-particle duality, where it is denoted ψ(position,time) and where | ψ | 2 is equal to the chance of finding the subject at a certain time and position.

For example, in an atom with a single electron, such as hydrogen or ionized helium, the wave function of the electron provides a complete description of how the electron behaves. It can be decomposed into a series of atomic orbitals which form a basis for the possible wave functions.

For atoms with more than one electron (or any system with multiple particles), the underlying space is the possible configurations of all the electrons and the wave function describes the probabilities of those configurations.

Wave-Particle Duality

In physics and chemistry, waveparticle duality is the concept that all energy (and thus all matter) exhibits both wave-like and particle-like properties. Being a central concept of quantum mechanics, this duality addresses the inadequacy of classical concepts like “particle” and “wave” in fully describing the behavior of quantum-scale objects.

Orthodox interpretations of quantum mechanics explain this ostensible paradox as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent, second-order consequence of various limitations of the observer.

This treatment focuses on explaining the behavior from the perspective of the widely used Copenhagen interpretation, in which waveparticle duality is one aspect of the concept of complementarity, that a phenomenon can be viewed in one way or in another, but not both simultaneously.

The idea of duality originated in a debate over the nature of light and matter dating back to the 1600s, when competing theories of light were proposed by Christiaan Huygens and Isaac Newton: light was thought either to consist of waves (Huygens) or of corpuscles/particles (Newton).

Through the work of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, and many others, current scientific theory holds that all particles also have a wave nature (and vice versa).

This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. In fact, according to traditional formulations of non-relativistic quantum mechanics, waveparticle duality applies to all objects, even macroscopic ones; but because of their small wavelengths, the wave properties of macroscopic objects cannot be detected.

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