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Phase Factor
For any complex number written in polar form (such as ), the phase factor is the complex exponential factor (). As such, the term "phase factor" is related to the more general term phasor, which may have any magnitude (i.e. not necessarily on the unit circle in the complex plane). The phase factor is a unit complex number, i.e. a complex number of absolute value 1. It is commonly used in quantum mechanics. The variable appearing in such an expression is generally referred to as the phase. Multiplying the equation of a plane wave by a phase factor shifts the phase of the wave by : e^ A\,e^ = A\,e^. In quantum mechanics, a phase factor is a complex coefficient that multiplies a ket , \psi\rangle or bra \langle\phi, . It does not, in itself, have any physical meaning, since the introduction of a phase factor does not change the expectation values of a Hermitian operator. That is, the values of \langle\phi, A , \phi\rangle and \langle\phi, e^ A e^ , \phi\rangle are t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number a+bi, is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
