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Raptor112
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Homework Statement
It is known that ##M_1,M_2, M_3## commute with each other but I don't see how the second line is achieved even though it says that it's using that ##M_1## and ##M_2## commute?
Commuting Operators: Understanding How M1,M2 & M3 Work Together
- Thread starter Raptor112
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In summary, the conversation discusses how to rewrite an expression using the fact that ##M_1## and ##M_2## commute. The suggestion is to use the expression ##M_2 + M_1M_2## and rewrite it as ##(1 + M_1)M_2##, which can be simplified further.
It is known that ##M_1,M_2, M_3## commute with each other but I don't see how the second line is achieved even though it says that it's using that ##M_1## and ##M_2## commute?
- #2
TSny
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Note M2(1+M1) = M2 + M2M1
How can you rewrite the right hand side using the fact that M1 and M2 commute?
How can you rewrite the right hand side using the fact that M1 and M2 commute?
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Raptor112
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TSny said:
##M_2 + M_1M_2##
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OK. Can you see something you can do with this expression that will help?Raptor112 said:
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Raptor112
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##(1 +M_1)M_2## ?TSny said:
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Yes.
1. What are commuting operators?
Commuting operators are operators in quantum mechanics that share the same set of eigenstates, meaning that they can be measured simultaneously without affecting each other's results.
2. How do M1, M2, and M3 work together?
M1, M2, and M3 are commuting operators that represent different physical quantities, such as position, momentum, and energy. These operators can be used together to determine the state of a quantum system and how it evolves over time.
3. Why is understanding commuting operators important?
Understanding commuting operators is important because it allows us to make accurate predictions about the behavior of quantum systems and how they interact with each other. It is also a fundamental concept in quantum mechanics and is essential for many applications in physics and technology.
4. How are commuting operators related to quantum uncertainty?
Commuting operators play a crucial role in the Heisenberg uncertainty principle, which states that certain pairs of physical quantities, such as position and momentum, cannot be known precisely at the same time. This is because their respective operators do not commute, meaning that measuring one will affect the other.
5. Can commuting operators be used to describe all quantum systems?
No, commuting operators can only fully describe a quantum system if the system is in a stationary state, meaning that its properties do not change over time. For non-stationary systems, additional operators are needed to fully describe their behavior.
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