Matter wave
In quantum mechanics, a branch of physics, a matter wave is when you think of matter as a wave. The concept of matter waves was first introduced by Louis de Broglie. Matter waves are hard to visualize, because we are used to thinking of matter as a physical object. De Broglie revolutionized quantum mechanics by producing the equation for matter waves.
Wavelength of Matter
As experiments on light revealed that photons possessed both wavelike and particular properties, they were considered at the time to have a dual nature as both particles and waves. De Broglie showed that matter might exhibit such a 'wave-particle duality' as well. Basing his formula on earlier formulas, he arrived at the equation below.
[math]\displaystyle{ \lambda=\frac{h}{mv} }[/math]
Where λ is the wavelength of the object, h is Planck's constant, m is the mass of the object, and v is the velocity of the object. An alternate and also correct version of this formula is
[math]\displaystyle{ \lambda=\frac{h}{p} }[/math]
Where p is the momentum. (Momentum is equal to mass times velocity). These equations merely say that matter exhibits a particle-like nature in some circumstances, and a wave-like characteristic at other times. Erwin Schrödinger created an advanced equation based on this formula and the Bohr model, known as the Schrödinger equation.
Matter Wave Media
Position space probability density of an initially Gaussian state moving in one dimension at minimally uncertain, constant momentum in free space.
Matter wave double slit diffraction pattern building up electron by electron. Each white dot represents a single electron hitting a detector; with a statistically large number of electrons interference fringes appear.
Some trajectories of a particle in a box according to Newton's laws of classical mechanics (A), and matter waves (B–F). In (B–F), the horizontal axis is position, and the vertical axis is the real part (blue) and imaginary part (red) of the wavefunction. The states (B,C,D) are energy eigenstates, but (E,F) are not.
