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The wave function of an initially very localized free particle. In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively). Wave functions are complex ...
The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. [ 1 ] : 1–2 Its discovery was a significant landmark in the development of quantum mechanics .
Defining equation SI unit Dimension Wavefunction: ψ, Ψ To solve from the Schrödinger equation: varies with situation and number of particles Wavefunction probability density: ρ = | | = m −3 [L] −3: Wavefunction probability current: j: Non-relativistic, no external field:
The term "wave function" is typically used for a different mathematical representation of the quantum state, one that uses spatial coordinates also called the "position representation". [9]: 324 When the wave function representation is used, the "reduction" is called "wave function collapse".
Then solve the differential equation representing this eigenvalue problem in the coordinate basis, for the wave function | = (), using a spectral method. It turns out that there is a family of solutions. In this basis, they amount to Hermite functions, [6] [7] =!
In the Schrödinger picture, the wave function or field is the solution to the Schrödinger equation; = ^ one of the postulates of quantum mechanics. All relativistic wave equations can be constructed by specifying various forms of the Hamiltonian operator Ĥ describing the quantum system .
The concept of universal wavefunction was introduced by Hugh Everett in his 1956 PhD thesis draft The Theory of the Universal Wave Function. [8] It later received investigation from James Hartle and Stephen Hawking [9] who derived the Hartle–Hawking solution to the Wheeler–DeWitt equation to explain the initial conditions of the Big Bang ...
In non-relativistic quantum mechanics, the probability current j of the wave function Ψ of a particle of mass m in one dimension is defined as [2] = = {} = {}, where ℏ {\displaystyle \hbar } is the reduced Planck constant ;