Everything about Wave Function totally explained
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 (for example 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.
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.
Definition
The modern usage of the term
wave function refers to a
complex vector or
function, for example an element in a complex
Hilbert space. Typically, a wave function is either:
- a complex vector with finitely many components
» , the orthonormality condition holds similarly:
»
We have the analogous identity
»
Ontology
Whether the wave function is real, and what it represents, are major questions in the
interpretation of quantum mechanics. Many famous physicists have puzzled over this problem, such as
Erwin Schrödinger,
Albert Einstein and
Niels Bohr. Some approaches regard it as merely representing information in the mind of the observer. Others argue that it must be objective.
Further Information
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