Quantum mechanics(expected probability)

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SUMMARY

The discussion centers on calculating the probability of a specific state of a particle in quantum mechanics, specifically determining the probability of the first particle being in state A1 given a composite state |C>. The relationship between the probabilities of states A and B is defined as a linear combination, expressed as P(C) = aP(A) + bP(B). The user struggles with the mathematical representation of this relationship and seeks clarification on using inner products, such as , in their calculations.

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  • Familiarity with probability theory as it applies to quantum states.
  • Knowledge of linear algebra concepts, including inner products and vector spaces.
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Homework Statement



suppose we have two particles, first with probable states A1,A2,A3 and state B1,B2,B3 each with a certain probability P
Now if we know the probability of composite state |C> is Q
what is the probability to get the first particle to be A1?

im troubled. please help thanks

Here ,probability of getting C is any linear combination of A and B = aP(A)+bP(B)

Homework Equations





The Attempt at a Solution


i have tried to do like this
because C equals one of these 9 states (A1,A2,A3)+(B1,B2,B3)
lets call them |1>,|2>,...,|9>

i don't know how to relate use the "resultant" prbability to get back the original component probability

is it correct to use, for example <C|1> in calculation, I am in trouble
 
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You have a very fuzzy explanation of the problem, but isn't it as simple as (A1,Bi) summed over i?
 

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