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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 ...
While the time-evolution process represented by the Schrödinger equation is continuous and deterministic, in that knowing the wave function at one instant is in principle sufficient to calculate it for all future times, wave functions can also change discontinuously and stochastically during a measurement. The wave function changes, according ...
The condition m=0 is ruled out because = everywhere, meaning that the particle is not in the potential at all. Negative integers are also ruled out since they can easily be absorbed in the normalization condition. We then normalize the wave function, yielding a result where =. The normalized wave function is
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics.
The following equations have solutions which satisfy the superposition principle, that is, the wave functions are additive. Throughout, the standard conventions of tensor index notation and Feynman slash notation are used, including Greek indices which take the values 1, 2, 3 for the spatial components and 0 for the timelike component of the ...
The Coulomb wave equation for a single charged particle of mass is the Schrödinger equation with Coulomb potential [1] (+) = (),where = is the product of the charges of the particle and of the field source (in units of the elementary charge, = for the hydrogen atom), is the fine-structure constant, and / is the energy of the particle.
The time-independent Schrödinger equation for the wave function is ^ = [+ ()] = (), where Ĥ is the Hamiltonian, ħ is the reduced Planck constant, m is the mass, E the energy of the particle. The step potential is simply the product of V 0 , the height of the barrier, and the Heaviside step function : V ( x ) = { 0 , x < 0 V 0 , x ≥ 0 ...
Wave functions that fulfill this constraint are called normalizable. The Schrödinger equation, describing states of quantum particles, has solutions that describe a system and determine precisely how the state changes with time. Suppose a wave function ψ(x, t) gives a description of the particle (position x at a given time t).