Probabilities in Quantum Mechanics

In summary, when a large number of particles are sent through two slits with equal probabilities, the average result is that half go through each slit. This result is verified by repeating the experiment with another large number of particles and finding similar statistics. The law of large numbers ensures that the predicted probabilities will hold true even with further trials, as they will eventually converge to the expected result.
  • #1
StevieTNZ
1,934
883
Hi there,

The average expected result for particles with 1/2 probability going through slit 1 and 1/2 probabiltiy going through 2, for a large number of particles (N) is exactly that: 1/2 slit 1, 1/2 slit 2.

We send the large number of particles through and find that roughly half go through slit 1 and half go through slit 2. But we further send another N number of particles through.

When these sort of predictions get verified, do a further N number of particles get sent through and the statistics stay roughly the same as the first N lot of particles? Is that how the average is verified?

Because couldn't you get different probabilities if you send a further N number of particles through and they deviate away from 1/2 slit 1, 1/2 slit 2?
 
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  • #2
Is it that after a finite N number of trials, the probabilities predicted are more-or-less met, and with the law of large numbers, any further trials will still conform to the predicted statistics?
 

FAQ: Probabilities in Quantum Mechanics

What is the basis of probability in quantum mechanics?

In quantum mechanics, probabilities are based on the wave function, which describes the probability of finding a particle in a certain state. This wave function is represented by a complex-valued mathematical function.

How is probability interpreted in quantum mechanics?

In quantum mechanics, probability is interpreted as the likelihood of a particle being in a certain state when observed. This is known as the collapse of the wave function, where the particle's state is determined upon measurement.

What is the uncertainty principle and how does it relate to probability in quantum mechanics?

The uncertainty principle states that it is impossible to know both the position and momentum of a particle with absolute certainty. This relates to probability in quantum mechanics because it shows that there is always a level of uncertainty in the measurement of a particle's state, and probability is used to describe this uncertainty.

How do probabilities in quantum mechanics differ from classical probabilities?

In classical mechanics, probabilities are based on known and measurable variables, while in quantum mechanics, probabilities are based on the wave function and the uncertainty principle. Classical probabilities are also deterministic, meaning that the outcome can be accurately predicted, while quantum probabilities are probabilistic and only describe the likelihood of a certain outcome.

Can probabilities in quantum mechanics be calculated exactly?

No, probabilities in quantum mechanics cannot be calculated exactly. The uncertainty principle and the probabilistic nature of quantum mechanics make it impossible to know the exact outcome of a measurement. Instead, probabilities are used to describe the likelihood of a particle being in a certain state when observed.

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