- #1
subny
- 16
- 0
Homework Statement
Homework Equations
i think the most relevant equations would be some commutator algebra theorems i do not know of !
Challenging commutator algebra problem in quantum mechanics
- Thread starter subny
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Homework Help Overview
The discussion revolves around a commutator algebra problem in quantum mechanics, specifically involving the exponential of an operator and its interaction with another operator.
Discussion Character
- Exploratory, Mathematical reasoning
Approaches and Questions Raised
- Participants explore the definition of the exponential of an operator and its application in the context of commutators. There is a focus on how to utilize the series expansion of the exponential function in calculations involving operators.
Discussion Status
Some participants have provided definitions and suggested ways to manipulate the series expansion to progress in the problem. There is an ongoing exploration of how to apply these concepts without reaching a definitive conclusion.
Contextual Notes
Participants are navigating through the definitions and properties of operators in quantum mechanics, with an emphasis on commutation relations and the implications of those relations in their calculations.
i think the most relevant equations would be some commutator algebra theorems i do not know of !
- #2
- 22,170
- 3,327
What is the definition of ##e^{\lambda A}##? Use that.
- #3
subny
- 16
- 0
you mean this - http://en.wikipedia.org/wiki/Exponential_function#Formal_definition
ok so how to use that here
ok so how to use that here
- #4
- 22,170
- 3,327
So ##e^{\lambda A} = \sum_{n=0}^{+\infty} \frac{\lambda^n A^n}{n!}##
So can you calculate ##e^{\lambda A}B## now? Just multiply the series with B and apply that ##AB = BA + cI##.
So can you calculate ##e^{\lambda A}B## now? Just multiply the series with B and apply that ##AB = BA + cI##.