A wave function or wavefunction is a probability amplitude in quantum mechanics describing
the quantum state of a particle and how it behaves. Typically, its values are complex numbers
and, for a single particle, it is a function of space and time.
The laws of quantum mechanics (the Schrödinger equation) describe how the wave function
evolves over time.
The wave function behaves qualitatively like other waves, like water waves or waves on a
string, because the Schrödinger equation is mathematically a type of wave equation. This
explains the name "wave function", and gives rise to wave–particle duality.
The most common symbols for a wave function are ψ or Ψ (lower-case and capital psi).
Although ψ is a complex number, |ψ|2 is real, and corresponds to the probability density of
finding a particle in a given place at a given time, if the particle's position is measured.
The SI units for ψ depend on the system. For one particle in three dimensions, its units are m–
3/2. These unusual units are required so that an integral of |ψ|2 over a region of three-
dimensional space is a unitless probability (i.e., the probability that the particle is in that
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For different numbers of particles and/or dimensions, the units may be different (though can
be determined by dimensional analysis).
The wave function is central to quantum mechanics, because it is a fundamental postulate of
quantum mechanics. It is the source of the mysterious consequences and philosophical
difficulties in the interpretations of quantum mechanics—topics that continue to be debated
Wave Definition :-
A disturbance causing energy transfer from one point to another without the actual movement
of particle is called a wave. There are two modes of energy transfer
1. Particle motion
2. wave motion.
When no particle is transferred from one part of space to other although energy is transferred
then we call it wave or simply wave.
The disturbance can be by natural reasons like air, wind, storm etc or it can be caused
intentionally. A wave can be of many times like transverse wave and longitudinal wave etc.
During energy transfer of the wave from one point to another, the wave possesses the energy.
This energy is called wave energy.
Waves Properties :-
Transmission and media :- The movement of the wave is mostly rectilinear or in a straight
line. It can travel through various medium like gas, liquid etc. a medium can be a bounded
medium, a linear medium, an uniform medium, an isotropic and an anisotropic medium. These
are also called as the transmission medium.
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It under goes the following phenomena namely reflection, interference, absorption, refraction,
diffraction, polarization, dispersion.
1. Reflection:- The properties of reflection on a mirror are also followed by a wave. When a
wave reflects then the angle of incidence is equal to angle of reflection.
2. Interference:- when waves of equal frequency and nearly equal amplitude are
superimposed then the phenomenon of interference occurs. It can be of two types viz.
constructive and destructive interference.
3. Absorption :- The property of absorption is also followed during wave motion. It can be
absorbed by some surface leading to the change in the type of energy.
4. Refraction :- While traveling from one medium to another the wave may change its speed.
This property is called refraction. The amount of refraction is dependent on the refractive
index of the medium.
5. Diffraction:- The phenomenon of spreading of wave when it passes or emerges from an
opening or it bends when it encounters an obstacle is called diffraction. These effects are
more significant if the size of the opening is comparable to the wave’s wavelength.
6. Polarization:- A wave oscillating in one plane or direction is called a polarized wave. It can
be circular polarized or plane polarized. Even we can use the polarization filter for this
7. Dispersion :- The phenomenon of dispersion is also followed by the wave. Dispersion is
the breaking into the component colors like when the white light passes through the prism
then it is dispersed into 7 colors.
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