Lesson plan
Phase factor
In physics and representation theory, a phase factor is a multiplier representing the phase of a wave or the phase difference between two quantities. It is formulated as a unit complex number, that is a complex number with absolute value . For a complex number written in polar form, such as , the phase factor is the complex exponential, , where the variable is the phase and is the imaginary unit. If a quantity like a scalar, vector, or a matrix (representing a wave, state, or operator) is equal to another quantity times a phase factor, then those two quantities are said to be equivalent up to the phase factor, as it leaves the length (or norm) unchanged. As a set, the possible phase factors form the circle group U(1) , but the term often refers to a scalar recording a phase choice or convention, or an ambiguity in choosing a representative.
Article summary
In physics and representation theory, a phase factor is a multiplier representing the phase of a wave or the phase difference between two quantities. It is formulated as a unit complex number, that is a complex number with absolute value . For a complex number written in polar form, such as , the phase factor is the complex exponential, , where the variable is the phase and is the imaginary unit. If a quantity like a scalar, vector, or a matrix (representing a wave, state, or operator) is equal to another quantity times a phase factor, then those two quantities are said to be equivalent up to the phase factor, as it leaves the length (or norm) unchanged. As a set, the possible phase factors form the circle group U(1) , but the term often refers to a scalar recording a phase choice or convention, or an ambiguity in choosing a representative.
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
No sources recorded.
Key claims and bibliography are generated from the same tracked claims and sources as the article page.