Quantum Mechanics: Probablities

In summary, classical probabilities assume certainty in determining the state of a system, while quantum probabilities consider the uncertainty of quantum systems. The uncertainty principle in quantum mechanics states that probabilities represent the likelihood of a particle's position or momentum, rather than a specific value. Probabilities cannot predict the exact outcome of a quantum system, as it is determined randomly. Superposition in quantum mechanics allows a particle to exist in multiple states, with probabilities determining the likelihood of a particular state. The measurement problem in quantum mechanics relates to probabilities as the act of measurement can change a particle's state, making the exact outcome unpredictable.
  • #1
Robben
166
2
Suppose we have a spin##-1## particle in a certain state ##|\phi\rangle## under the ##S_z## basis. How do you find the probabilities that a measurement of ##S_z## will result in the values of ##\hbar,0,## or ##-\hbar##?

Also, what does it mean exactly when it says what is the probability that ##S_x## will result in the value of ##\hbar## in this state?
 
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  • #2
Could it be that this question should be put to the homework section of these forums?
 

Related to Quantum Mechanics: Probablities

1. What is the difference between classical and quantum probabilities?

Classical probabilities are based on the assumption that the state of a system can be determined with complete certainty, while quantum probabilities take into account the inherent uncertainty of quantum systems.

2. How do probabilities factor into the uncertainty principle in quantum mechanics?

The uncertainty principle states that it is impossible to know both the position and momentum of a particle simultaneously. Probabilities in quantum mechanics represent the likelihood of a particle's position or momentum being in a certain range, rather than a specific value.

3. Can probabilities predict the exact outcome of a quantum system?

No, probabilities in quantum mechanics can only predict the likelihood of a particular outcome. The actual outcome of a quantum measurement is determined randomly.

4. How is the concept of superposition related to probabilities in quantum mechanics?

In quantum mechanics, a particle can exist in a state of superposition, meaning it can simultaneously occupy multiple states. Probabilities are used to determine the likelihood of a particle being in a particular state when it is measured.

5. How does the measurement problem in quantum mechanics relate to probabilities?

The measurement problem in quantum mechanics arises from the fact that the act of measuring a particle can change its state. Probabilities are used to predict the likely outcomes of measurements, but the exact outcome cannot be determined due to the unpredictability of quantum systems.

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