# Quantum mechanics(expected probability)

• member 141513
In summary, the conversation discusses the probability of a composite state |C> being a linear combination of two particles with probable states A1, A2, A3 and B1, B2, B3 respectively. The probability of getting the first particle to be in state A1 is equal to the sum of probabilities of all the possible combinations of A1 and Bi. The speaker is unsure how to use the "resultant" probability to calculate the original component probabilities.
member 141513

## 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?

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

## 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

You have a very fuzzy explanation of the problem, but isn't it as simple as (A1,Bi) summed over i?

## What is quantum mechanics?

Quantum mechanics is a branch of physics that studies the behavior of particles at a very small scale, such as atoms and subatomic particles. It explains how these particles behave and interact with each other on a quantum level, which is different from the classical mechanics that we observe in our everyday lives.

## What is the expected probability in quantum mechanics?

The expected probability in quantum mechanics refers to the likelihood of a particular outcome or measurement of a quantum system. It is calculated using mathematical equations and is often represented by the wave function of the system, which describes the probability of finding the system in a particular state.

## How is quantum mechanics related to Heisenberg's uncertainty principle?

Heisenberg's uncertainty principle is a fundamental principle in quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a particle. This is because measuring one quantity with high accuracy will inherently lead to uncertainty in the other. This principle arises from the wave-particle duality of quantum particles.

## What are quantum superpositions?

Quantum superpositions refer to the phenomenon in which a particle or system exists in multiple states or positions simultaneously. This is a fundamental concept in quantum mechanics and is often illustrated by the famous Schrödinger's cat thought experiment. Superpositions are described by the wave function and are only observed when the system is not being observed or measured.

## How is quantum mechanics used in technology?

Quantum mechanics has numerous applications in technology, such as in the development of semiconductors, transistors, and lasers. It also plays a crucial role in quantum computing, which has the potential to revolutionize computing power and solve complex problems that are not possible with classical computers. Additionally, quantum mechanics is used in medical imaging, cryptography, and other fields of science and technology.

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