- #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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The discussion centers on solving a commutator algebra problem in quantum mechanics, specifically involving the expression e^{\lambda A}. Participants reference the formal definition of the exponential function and suggest using the series expansion to approach the problem. The key step involves calculating e^{\lambda A}B by multiplying the series with B and applying the commutation relation AB = BA + cI. This method aims to simplify the calculation and derive the desired results. The conversation emphasizes the importance of understanding commutator algebra theorems in quantum mechanics.
i think the most relevant equations would be some commutator algebra theorems i do not know of !
- #2
- 22,169
- 3,328
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
- 22,169
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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##.
for d), I am a bit confused. I have two trains of thoughts here
any thoughts on which answer is correct, and why the other one is incorrect? Both seem like valid solutions to me. Or is the question ambiguous?
thanks