EIGENFUNCTION Meaning and
Definition
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An eigenfunction is a fundamental concept in mathematics, specifically within the field of linear algebra. It refers to a function that, when operated upon by a linear operator, produces a scalar multiple of itself. In other words, an eigenfunction remains unchanged, except for being multiplied by a constant factor, when subjected to a certain mathematical operator.
Eigenfunctions are crucial in various areas of mathematics and the natural sciences, particularly in the study of differential equations. They are typically used to solve equations and understand the behavior of systems under specific conditions. Each eigenfunction is associated with a corresponding eigenvalue, which represents the scalar factor by which the function is transformed.
The term "eigenfunction" is derived from the German words "eigen," meaning "own" or "specific," and "funktion," meaning "function." Together, they emphasize the unique and individual nature of these functions with respect to a given operator.
A notable application of eigenfunctions is found in quantum mechanics, where the wave function describing the behavior of a particle can be expressed as a linear combination of eigenfunctions. These eigenfunctions, known as stationary states, help determine the possible energy levels of a quantum system and enable the calculation of probabilities associated with various outcomes.
Overall, eigenfunctions play a fundamental role in many areas of mathematics and science, providing a powerful tool to understand and analyze various mathematical operators and physical phenomena.
Common Misspellings for EIGENFUNCTION
- wigenfunction
- sigenfunction
- digenfunction
- rigenfunction
- 4igenfunction
- 3igenfunction
- eugenfunction
- ejgenfunction
- ekgenfunction
- eogenfunction
- e9genfunction
- e8genfunction
- eifenfunction
- eivenfunction
- eibenfunction
- eihenfunction
- eiyenfunction
- eitenfunction
- eigwnfunction
- eigsnfunction
Etymology of EIGENFUNCTION
The word "eigenfunction" comes from the combination of two German words: "eigen", meaning "own" or "characteristic", and "Funktion", meaning "function". The term was coined by the German mathematician David Hilbert in the early 20th century as he was studying functional analysis and related concepts in mathematics. It is commonly used in mathematical physics and quantum mechanics to refer to a function that remains unchanged, up to a scalar factor, when acted upon by a specified operator.
