How do you find the wave function of a particle?
The wavefunction of a light wave is given by E(x,t), and its energy density is given by |E|2, where E is the electric field strength. The energy of an individual photon depends only on the frequency of light, ϵphoton=hf, so |E|2 is proportional to the number of photons.
What is the wave function of an electron?
In quantum mechanics, the physical state of an electron is described by a wave function. According to the standard probability interpretation, the wave function of an electron is probability amplitude, and its modulus square gives the probability density of finding the electron in a certain position in space.
What is the wave equation of an electron?
Apply the de Broglie wave equation λ=hmv λ = h m v to solve for the wavelength of the moving electron.
What is the wave function equation?
To find the amplitude, wavelength, period, and frequency of a sinusoidal wave, write down the wave function in the form y(x,t)=Asin(kx−ωt+ϕ). The amplitude can be read straight from the equation and is equal to A. The period of the wave can be derived from the angular frequency (T=2πω).
How do you find the wavelength of a wave function?
The wavelength can be found using the wave number (λ=2πk). ( λ = 2 π k ) .
Who calculated wave functions for electrons?
Schrödinger
Schrödinger subsequently showed that the two approaches were equivalent. In 1926, Schrödinger published the famous wave equation now named after him, the Schrödinger equation.
Do wave functions have mass?
Yes. In fact the evolution of the wave as it travels is dependent on the mass. The Schrödinger equation uses the kinetic energy to control how the wave changes with time, and the kinetic energy in turn is a function of the mass.
How do you find the wavelength of an electron given kinetic energy?
Suppose an electron has momentum equal to p, then its wavelength is λ = h/p and its frequency is f = E/h. (ChemTeam comment: note the use of the two de Broglie equations.) Now comes the question: Should not the velocity of an electron be v = p/m? (ChemTeam comment: replace p with mv to get mv/m = v.)
How does a wave have mass?
A water wave is not a packet of water traveling along. In this way, waves can have no mass but still carry momentum. In addition to being a particle, light is also a wave. This allows it to carry momentum, and therefore energy, without having mass.