EIGENSTATE Meaning and
Definition
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An eigenstate is a fundamental concept in quantum mechanics, representing a specific state of a quantum system. It is a state in which a physical property (such as position, momentum, or energy) of a quantum particle is well-defined and can be measured precisely. In other words, an eigenstate is a state that corresponds to a specific eigenvalue of an operator associated with the observable being measured.
Within the framework of quantum mechanics, physical quantities are represented by Hermitian operators, and the eigenstates of these operators are the states in which the observable yields a definite value when measured. For example, if we consider the position of a particle, the eigenstate is represented by a spatial distribution in which the position of the particle is known with certainty.
Eigenstates play a crucial role in the mathematical formulation of quantum mechanics, as they form a basis for the state space of a quantum system. Any state of the system can be expressed as a linear combination of eigenstates, and the coefficients of this linear combination determine the probability of measuring a particular value when the observable corresponding to the eigenstates is measured.
Eigenstates are often represented in terms of wave functions or state vectors in a Hilbert space, which provide a mathematical description of the quantum system. These wave functions evolve in time according to the Schrödinger equation, allowing for predictions of future behavior and measurement outcomes. By studying the properties of eigenstates and their associated eigenvalues, physicists gain insights into the behavior and properties of quantum systems.
Common Misspellings for EIGENSTATE
- wigenstate
- sigenstate
- digenstate
- rigenstate
- 4igenstate
- 3igenstate
- eugenstate
- ejgenstate
- ekgenstate
- eogenstate
- e9genstate
- e8genstate
- eifenstate
- eivenstate
- eibenstate
- eihenstate
- eiyenstate
- eitenstate
- eigwnstate
- eigsnstate
Etymology of EIGENSTATE
The term "eigenstate" is derived from the German word "eigen", meaning "own" or "inherent", and the word "state". In the context of quantum mechanics, an eigenstate refers to a physical state in which a quantum system possesses a defined value for a particular observable quantity, such as position or energy. The concept was first introduced in the 1920s by German physicist Max Born and further developed by Werner Heisenberg and Erwin Schrödinger, among others, leading to the establishment of quantum theory. Therefore, the word "eigenstate" combines the German and English words to form a term that specifically describes a distinct state of a quantum system.
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