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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 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".
However, even in this case the total wave function is dependent on time as explained in the section on linearity below. In the language of linear algebra , this equation is an eigenvalue equation . Therefore, the wave function is an eigenfunction of the Hamiltonian operator with corresponding eigenvalue(s) E {\displaystyle E} .
The quantum wave equation can be solved using functions of position, (), or using functions of momentum, () and consequently the superposition of momentum functions are also solutions: = + The position and momentum solutions are related by a linear transformation, a Fourier transformation. This transformation is itself a quantum superposition ...
Wave functions of the electron in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space, only the probability of finding it at different locations. [1] The brighter areas represent a higher probability of finding the electron.
A fundamental physical constant occurring in quantum mechanics is the Planck constant, h. A common abbreviation is ħ = h /2 π , also known as the reduced Planck constant or Dirac constant . Quantity (common name/s)
The quantum harmonic oscillator is the quantum ... Another illustration of the time propagation of the common wave function for three different atoms emphasizes the ...
The definition of quantum theorists' terms, such as wave function and matrix mechanics, progressed through many stages.For instance, Erwin Schrödinger originally viewed the electron's wave function as its charge density smeared across space, but Max Born reinterpreted the absolute square value of the wave function as the electron's probability density distributed across space; [3]: 24–33 ...